{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Searching the lost plane MH370 by bayesian method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "There was a very serious and tragic air crash in 2014. The MH370 flight planned from Kuala Lumpur to Beijing lost its signal about 40 minutes after takeoff and eventually failed to reach the end of the flight to Beijing. Many countries in the vicinity of the missing plane has been searching for the first time, but no sign of the plane has been found. Until four years later, MH370 is still a mystery, still no traces of the aircraft found.There are many reasons for not finding the plane that crashed. One of the important reasons for this is that the search area is inaccurate, which means that the location and search scheme of the wrecked aircraft may greatly affect the efficiency of the search. So we considered the process of the plane crash as a physical model, and when the plane crashed into the ocean,we try to use Bayesian search to the plane.\n",
    "\n",
    "## Analysis of the Problem\n",
    "For finding a missing aircraft, we can split it into two part: First, we have to predict the descending route of the aircraft and the searching area; Then, we have to calculate the probability of each area. Also, after some discussion, we came to the conclusion that we should consider the possibility of turning during gliding and taxiing. Each area does not have the some probability, we use the bayesian networks model. This model can represent the probabilistic relationship between the probability and the sliding distance and the deviation from the predetermined trajectory.\n",
    "\n",
    "## Assumption\n",
    "###  Wind and ocean currents\n",
    "For a whole range of search areas, the effect of ocean currents is weak, and we will not consider the impact of ocean currents on the displacement of falling aircraft in the sea.\n",
    "And also no considering of the wind in the course of the plane’s descent.\n",
    "<br>\n",
    "### Plane crash process\n",
    "\n",
    "#### Assumption of aircraft falling outside conditions\n",
    "\n",
    "Assuming the plane doesn’t disintegrate during the falling.\n",
    "The last time signal of MH370 was at sea, according to MH370 ’s flight route, we assumed that the plane would crash into the ocean rather than land.\n",
    "After the aircraft engine failure, the fall direction and velocity direction are the same, no deviation in the direction.\n",
    "<br>\n",
    "#### Simple calculation of the falling position of aircraft\n",
    "the following symbol are appear in our equations to solve the problem.\n",
    "\n",
    "[![symbol.png](https://i.loli.net/2018/06/11/5b1d6b99a0e86.png)](https://i.loli.net/2018/06/11/5b1d6b99a0e86.png)\n",
    "\n",
    "we assume that, after the aircraft’s engine failed, the fuel ran out and the plane started to fall without power but it still has a speed. and then, we have a force analysis of aircraft. The plane will be subjected to the force of gravity(Mg) and air(F).The force of air on an aircraft can be broken down into vertical lift and horizontal resistance.[3] As shown in Figure.<br>\n",
    "[![606.png](https://i.loli.net/2018/06/11/5b1d6f360d5ef.png)](https://i.loli.net/2018/06/11/5b1d6f360d5ef.png)<br>\n",
    "From the formula for calculating the lift of aircraft, we can draw: <center>$F_1 = \\frac{1}{2}C_1\\rho v^2S_1$</center><br>\n",
    "From the formula for calculating the resistance of aircraft, we can draw:<center>$f = \\frac{1}{2}C_f\\rho v^2 S_2$</center><br>\n",
    "Because atmospheric density varies according to altitude.After querying the relevant data, we obtained the formula between altitude and atmospheric density.<br>\n",
    "<center>$\\rho_H = \\rho_0(1 - 2.25577 \\times 10^{-5}H)^{4.25588}$</center><br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "since the last time the plane sent a signal, the flight altitude was 35000 feet (10668m) so we assume H = 10000m, and calculate $\\rho_H = 0.4007kg/m^3$\n",
    "then we can draw the graph of$\\rho_H$<br>\n",
    "[![603.png](https://i.loli.net/2018/06/11/5b1d70d663e53.png)](https://i.loli.net/2018/06/11/5b1d70d663e53.png)\n",
    "<br>\n",
    "from this graph, we can consider it to a linear model, and then find the average ρas the atmo- spheric density we use in this problem.\n",
    "then we can get:<br>\n",
    "<center>$ρ = \\frac{1.225 + 0.4007}{2} = 0.8129 ≈ 0.8 kg/m^3$<br></center>\n",
    "Next we’ll build a coordinate system:<br>\n",
    "The flight direction of the plane is X − axis; Vertical direction is Y − axis Next, we can decompose the acceleration according to the force direction. Finally, we have following equations:<br>\n",
    "<center>$f = Ma_x$, $Mg-F_1 = Ma_y$</center>\n",
    "<br>\n",
    "according to the formula for calculating velocity and acceleration,we can get:\n",
    "<br>\n",
    "<center>\n",
    "$\\begin{align*} v_x &= \\frac{dx}{dt} \\\\ a_x &= \\frac{d^2x}{dt^2} \\end{align*}$ \n",
    "</center>\n",
    "<br>\n",
    "\n",
    "in the same ways,\n",
    "<br>\n",
    "<center>\n",
    "$\\begin{align*}x &= v_x t \\\\ a_y &= \\frac{d^2 y}{dt^2} \\end{align*}$ \n",
    "</center>\n",
    "<br>\n",
    "\n",
    "Finally, we can get: \n",
    "<br>\n",
    "<center>\n",
    "$\\begin{align*}\\frac{1}{2}\\rho(\\frac{dx}{dt}^2 S_1 &= M \\frac{d^2x}{dt^2} \\\\\\frac{1}{2}\\rho(\\frac{dy}{dt}^2 S_2 &= M g - M\\frac{d^2x}{dt^2}  \\end{align*}$ \n",
    "</center>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can use matlab to solve these two differential equations.\n",
    "According to the plane of the MH370 flight, the information of the Boeing 777-200ER, we assume that$S_1 = 400m^2$; $S_2 = 300m^2$; $C_1 = 1.5$; $C_f = 0.09$; $ M = 200000kg$; $y(0) = 10000m$; $x(0) = 0$; $y'(0) = 0$;$ x'(0) = 250 m/s$<br>\n",
    "\n",
    "then we can get a graph of Plane Fall trajectory:<br>\n",
    "\n",
    "[![607.png](https://i.loli.net/2018/06/23/5b2df0aacee9b.png)](https://i.loli.net/2018/06/23/5b2df0aacee9b.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and also we can get the time $(t)$ of the plane from losing power to falling sea is $t = 117.0485s x = 17553m$, so the point that the plane fall into the sea is $(17553,0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents\n",
    "### Bayesian Method\n",
    "### Comparison of Search Methods\n",
    "In many search methods, we first consider the parallel sweep search method. If we have sufficient resources and can search without considering any time cost, a parallel sweep search method is\n",
    " 5\n",
    "available to find the crashed aircraft. But the rescue time is valuable, the scope is broad, the sea terrain is complex, so the use of this method of search efficiency will be very low, it is likely to miss the best rescue time. So we hope to be able to search and rescue from the place with the highest probability of plane crash. The Bayesian search method can calculate the probability of finding a crashed plane in comparison to the parallel sweep search method. According to the probability, we can search from high probability to low, in order to maximize the rescue time.<br>\n",
    "\n",
    "[![601.png](https://i.loli.net/2018/06/23/5b2df1174be9a.png)](https://i.loli.net/2018/06/23/5b2df1174be9a.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bayesian Search Method\n",
    "We give a bounded the search area and sperated them some disjoint sub-areas. Each sub-areas has it own specific probabilty of cataining the aircarft or its wreckage. This probability is also the initial probability. We also use Bayes’ Theorem to get the probability of finding the wreckage. The formula of Bayes’s Theorem is as follows:\n",
    "<br>\n",
    "<center>\n",
    "   $P(A|B) = \\frac{P(A \\cap B)}{P(B)} = \\frac{P(A)\\cap P(B)}{\\sum P(A)\\bullet P(B_i)}$ \n",
    "</center>\n",
    "<br>\n",
    "\n",
    "The posteriori probability is “finding hte plane” and the initial probability is “the plane or its wrckage is in this sub-areas. The theorem also has another explanation: If we get the $p$ as the probability that a sub-area is contain the plane, and if the plane is successfully found in this sub-area, we give it a new probability $q$. If we did not found the plane, we can use Bayes’theorem to update $p$ to $p′$:\n",
    "<br>\n",
    "<center>\n",
    "   $p' = \\frac{p(1-q)}{(1-p)+p(1-q)}$ \n",
    "</center>\n",
    "<br>\n",
    "\n",
    "For each sub-area, we assume that the probability before the searching is $r$, the prior probability). If this sub-area is been searched and the aircraft is not found, the probabilities of other sub-area will be increased and we assume the probability is $r′$(the posterior probaility). We can get a new formula:\n",
    "<br>\n",
    "<center>\n",
    "   $r' = \\frac{r}{1-pq} > r$ \n",
    "</center>\n",
    "<br>\n",
    "\n",
    "Through this formula, we can continually update our modal and the probabilties of the remain- ing sub-areas. What’s more, this formula also can renomalize the probability distribution, which means we have $100\\%$ confidence that the aircraft is in the sub-areas.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability of Containing\n",
    "Before we use the Bayes Search Method, we must first ensure which area the downed plane could be. That is the ’p’ in the function of Bayes Search Method. We need to get ratio between each small area and by this ratio a probability density function can be get. By the same time there is not only one possibility for the plane falling down. So we need to consider about all possibilitiesand calculate the weight of each possibility, then we can get the final probability that the plane is in that area. Then we can use Bayes Search Method too solve the problem.\n",
    "\n",
    "#### Two Dropping Model\n",
    "From our assumptions, the downed plane we are searching for cannot transmit signals. So we only can rely on the last signal from the plane that we received. Because the last contact of Malaysia Airlines Flight 370 was when the plane left the range of Malaysian Military radar while over the Andaman Sea. From the last radar detection we can get many important information about the downed plane, such as its direction, altitude, speed, and so on at last contact. From the last radar detection and those information we can form two generally reasonable guesses about how the plane behaved in the time immediately following. Then we will give you the two guesses in different condition as follow.\n",
    "\n",
    "#### Model 1: Flying Model\n",
    "The first model we consider about only the signals can’t be received that is the plan still can fly. This model is about the time after the plane can’t find by radio, it can fly until the fuel runs out of. That is the time and place it begins to fall into the ocean. Using the information such as, altitude, speed, direction, that we get from the final radar detection, we can compute how far the plane can fly after we can’t receive the signals before running out of fuel. Let the longest of the distance it can fly as D. As the Flying Model consider about the largest probability is the air plan uses all of its fuel to fly. Therefore we can assume that the largest probability of the distance it flies after can’t be detected by radio is the probability of D. For the direction it flies after can’t be detected by radio, the most likely one is to fly straight forward. Then we can get the probability of both sides is symmetry by the trajectory which fly straight forward.\n",
    "Let p1 be the un-normalized formula for the Flying Model. Then we can get:\n",
    "<br>\n",
    "<center>\n",
    "   $p_1=r\\cdot cos^2(\\theta/2), ~ ~ ~ ~ r\\in[0,D], ~ ~ ~ ~ \\theta\\in[-\\pi,\\pi]$ \n",
    "</center>\n",
    "<br>\n",
    "\n",
    "So when $r$ is $0$, the downed plane begins to fall at the point where we lost contact with the plane, and for any $\\theta$, $p_1 = 0$. When $r$ is $D$, that is the point the plane begins to fall is $D$ away from where it can’t detecte by radio, we can get the largest $p_1$. As the angle $\\theta$ farther away from zero, the $p_1$ become smaller. We show this probability in pictures.\n",
    "the red part in the picture is the area where have the highest probability , and purple part is the area where has the lowest probability.<br>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114073630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the optimistric distribution\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "fig = plt.figure()\n",
    "\n",
    "# 3d\n",
    "# ax = Axes3D(fig)\n",
    "\n",
    "ax = fig.add_subplot(111, projection='3d') # X, Y value\n",
    "X = np.linspace(-np.pi, np.pi)\n",
    "Y = np.linspace(0,10)\n",
    "X, Y = np.meshgrid(X, Y) \n",
    "R = Y * np.cos(X/2)**2\n",
    "# height value\n",
    "Z = Y * np.cos(X/2)**2\n",
    "# x-y\n",
    "# rstride: cstride:\n",
    "# rcount:50ccount:\n",
    "#vmaxvmin\n",
    "ax.plot_surface(X, Y, Z, rstride=1, cstride=1,cmap=plt.get_cmap('rainbow')) # zdir : 'z' | 'x' | 'y'\n",
    "# offset :\n",
    "ax.contourf(X,Y,Z,zdir='z',offset=-2) # zxy\n",
    "ax.set_zlim(-2,10)\n",
    "ax.set_ylim(0,10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model 2: Falling Model\n",
    "Then we will consider the second case. When the signal station receives the final signal from the plane, the plane has broken down, it may be directly down, as we assume in the $2^{nd}$ hypothesis, or it is possible to move forward briefly after the fall.\n",
    "So in the second case, the value of R will be between the displacement x of the plane falling directly and the maximum displacement Dof the plane. Next we consider the probability that there may be any aircraft remains in the area where the plane crashed. We use the following formula to calculate.\n",
    "<br>\n",
    "<center>\n",
    "    $p_2=(D-r)*cos^2(\\theta/2), ~ ~ ~ ~ r\\in[x,D], ~ ~ ~ ~ \\theta\\in[-\\pi,\\pi]$\n",
    "</center>\n",
    "<br>\n",
    "\n",
    "\n",
    "When $r$ takes a value of $x$, the direction of descent may not be fixed if it has a direct drop of the horizontal initial velocity, but once the plane breaks down and begins to fall, the direction cannot be adjusted again.\n",
    "We still use color to represent the probability of a plane falling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/oVV8Qd4hjZo5bNtmZmaGlZUVRkdH141IakS7BHmrdcrlMpOTk+RyOY4fP86ZM2ca3sHbIYD7SUTbTSdL0zzfjo3R3U58PupLv+rZz08sjuM0ZaTVqZTFz/7sz/LlL3+ZT37yk3z5y1/mfe97X9vW9gV5G5RSFIvFmg+sEKKWBshkMuvSANvRzgh5YxG8Ny2kUChw4sQJzp07t+UF2G4/ZA/Pg8OyrNpj904qDfaTuHdS3LZaeyc+H/WlX/U+H+0qy9vtMbeDZis4stlsyymLX/zFX+SZZ55hdXWV0dFRPvOZz/DJT36SD37wg/zJn/wJR48e5etf/3pL71GPL8ib4DVzOI7DlStXGB8fB2BqaopisbjtiKRGtDNC9uphvQaTcrm8qwaTdqcsPCGem5tjcHCQYDBIJpNZV2lQX2WwMS/qC3Jza29V+mVZVq3ZZW1tjWKxyPPPP79uyrXXVNHK5m6nK0Na2dRrVZD//M//vOHrTz/9dEvrboYvyBvY2MzhCcW1a9cQQnD8+HH6+vqauiDbGSGXy2VeeeUVLMvi5MmTOxrbtHGNdkTIrusyMzPD3Nwcw8PDPPbYY7V0Tv1F6m1gFQqFdXlR73G7UqmQz+drkyjeqrRL3OqFuq+vj0qlgpSSCxcuNGxPbsXno5M1yNC8IGcyGcbGxjpwRJ3DF2Q2b+bIZDJMTk7WIuIjR4609D7tEORcLsfU1BTlcpmLFy821ekHrQuylJJMJlM76es3Mht9xs3M0L0obm1tjaWlJaanp9eJgxdV3ytviUbspQh5p3h1wpu1J2/m86GUatg+Xv+36LQgN7v+3aiyaDdvaUHerJljdXWVqakpQqEQp0+fZmlpqS2+v60IciaTYWJiAoCRkREKhULTYgzNC7KUkrm5OWZnZwmHwxw9epTjx483fRyBQIDe3l4ikQgnT54kHA7XTGY285bwRDoWi+26E64ddFKQ75WPxXY+H97TzUYLzXrviE59L81GyLlcriObep3kLSnIXuma67q1Zg64XfA9PT1NIpFYN5JodXX1jmGPzdCMIKfT6drg0FOnTtHV1UUulyObzbZ0LLvN2dYL8dDQEI8++ijJZLItKZhGx+ZFcRvFoVQqUSgU1rUsN2qw6OQg1f1YsdBsKmQzZ7Z6n49UKkWhUOCFF16oCXv936LVDcVmj70dOeS7zVtKkBvVECulanaTvb29PPTQQ3dEw7qut0WQd3pSehOcJycnMU2T06dPr+v+alf+dyfU+yJ7Quxtxmma1pbvxTue7W4QmqYRi8WIxWLrXq9vsFhZWVk3SLVcLrOwsFATh3Y8Wu+Xzcd62r3xVu/zYRgGhmEwPj5eu2luHPPUDp+P3ZLNZttm+nO3eEsI8mZddd6IpKGhoYYG7B6GYdwxZbdTx7m6ulqb4Hz27Nk7xAf+eWJIJ6kX4sHBwYZ2nO2eGNKs0G2Wny4Wi1y9erXm8exZNnpVBp44NGNS/1aJkHdCfY63/qY5NDS07t94Qp3JZNYNTq3PT8disU19PnaLL8h7jEaG8I7jcOvWLZLJ5I7tJg3DoFgsdvQ4V1ZWmJycJBqNcuHChTumLNTjTQzpBN5Q1ZmZmU2F2KPdXhbtxjRNTNNct9Neb4JeKBTWmdTv9FH7rZSy2Ak72XTbzOfDdd3a081GQyZPpD2DetM0d/W9F4vFLa+jvciBFGSlFIVCgWq1SjQarTVzzMzMsLq6uu2IpI0YhtG2R/ONx+lNcE4kEly8eHFHHUntKp+rZ6MQbzUpxKOd9pudqkPeeCybVRls9qi90aktFovtS0HuZCVEK6OhdF3f0ucjl8shpeTq1au1NNTGiLpRwOCdS3ulMmenHChBrm/myGQypNNpxsbGmJqaIpfLcfToUcbHx3f9R2qnAHq1u8vLy0xNTdHd3c2DDz5IOBze8Rrt9JCoF+KBgYEdCbHH3RpyejfY6lHbi6ZTqRQzMzO1QQPXr19flxNtZcahR6fy052OkNvx2evx0lDBYJB0Os3FixcBah4fG/cL6n0+lFK1p5v9duM8EILcqJnDtm2SySSZTIbjx49v20q8Fe2KkL3jfPbZZ+nr6+PSpUtNldO1Y5adlBLLsnj22Wfp7+/flRB7vBXsNxtFcLlcjtnZWQYGBigUCuvaleu74GKx2J4ZotppQfYmkXdi7fro2zRNuru7t/T5+P73v88XvvAFbt26xXve8x7Onz/PL/zCL/ATP/ETTR/H7//+7/PHf/zHCCG4//77+eIXv9iWUtiN7GtB9tpDvShNCEE2m2VychLLsgiFQjzyyCMt3yVbFeT6KFRKyQMPPNCySX0rx7K4uFg7lsuXLzd9Mb0VBLkRSikMw6Cnp+cOX4lqtVqrn06lUuuGqNanPRrlpzs9T6/dUazHvZgWspF6n48PfehDPPnkk3zkIx/hS1/6ElevXm0plzw/P88f/MEfcO3aNcLhMB/84Af52te+xkc/+tGm19yMfS3I9SdvOp1mcnISwzBq41uuXr3alhO8WUGur9318rLXrl27Z9OMPSHu6+vj4Ycf5qWXXmrJZ7edqZP9xGbCKYQgFAoRCoXuyE+Xy2UKhUJtNl+5XK5VGNyNbsR7vanXLK20Tff09DA8PHzHZJdmj6NcLmOaJqVSiUOHDrW8ZiP2tSADrKysMDExQTQaXVcm5rpuwzH3zbBb4dlqgrNhGB2rkGiEUorFxUWmp6drQuylJrzP1eyF+laOkHdDfWlXPfUVBl5zRT6f5+WXX14XTbcjP93Kxtt2dHrA6b1yevM4fPgwv/Vbv8WRI0cIh8M8+eSTPPnkk21ZeyP7XpC9FMDGTbF2m6fvBG+C8/z8/KYldZ2okGjEVkLs0ep31I5ctsd+23xpx/FuzE9blsW1a9c4f/58Le2x0U6zXqh3k5/u9My7gzy+KZ1O841vfKO2Cf+BD3yAr3zlK3zkIx9py/r17HtBHhkZaSgqd/MCdxyHmZkZlpaWahOcNzuJ2inIjR6d64W4t7d3yxxxq4K8WZWFlBLbtnedm95PEXInzi9vXdM0N81PexUfnp0m0NCIaePx7eeURTNptXYaC/393/89x48fr7WO//zP/zw/+MEPfEFuxL2MrLyJIclkktHR0R1NcG6nBWe9MHiDVaemprYV4vo1WhXkehH1bgZTU1O1dnPTNGvlZF5U1+g72m8pi06cd1uJZn1+uq+vb93veJ4SjfLTnlDbtt2xa6XTKYvdlIR6tDNCPnLkCM8++yylUolwOMzTTz/Nww8/3Ja1N7LvBXk72ukv6621cYLzbppM2inIrusihKgJcU9Pz66qJlqtI/ZuCl6Dy+TkZO1m4NWAevaahUKB2dnZmveu12xRP215Pwlyp9bdrWjWC2/9bDevVdmLpjOZDIVCgUAgsK/y061s6tXXk7fCY489xvvf/34uXbqEYRg89NBD/Pqv/3pb1t7IvhfkrU5g0zRrJuitYhgGpVKJ+fl5UqnUroXYo52CvLi4yNzcHD09PU3VNLcjB1wul3n22Wfp6uqqHYNX4yyEqNlr1luF1lcd5HI5FhYWyGazpNNpuru7a2IRi8U6VqrVKp2KkNu17sZW5XK5zKlTp2o2AIVCgaWlJQqFwrpxT/WNLjs9tzuZDmll4vR9993XtuP4zGc+w2c+85m2rbcZe/NsbxNeuVqrglypVGoTOk6cONFUt5+HrustGRV50WgmkyEQCDTdXALNpyw8N7rr169TrVZ57LHH1j1Wbtch1ajqYGJigng8TjAYpFAokEwmmZiYWLeZ5f3ca7P6TuaQO1n2put6w8aKRuOe6p9ktstPd5JmuwD3o7EQHABB3i5CbqX0rX6Cs2dW32peqtkIud73oquri76+Po4fP95St1AzgpxOp7lx4wbBYJCzZ89y8+bNpnJ8jdB1/Q7XtvpmC2/8k2eQXi8U7XQJ245Ob+p1gq0qITaOe6o/Hu9Jxouovfx0vb+HlHLPmdPvRy9kOACCvBXNNnTUT3D22q7feOONtpTR7VaQlVIsLy8zOTlJV1dXza/5ypUrbR1Suh3ZbJYbN26g6zpnz54lHo/fMfKqFTbb1Nuq2cJ79E6n08zOztYcwTyhCAaD+yYvDZ199G9m7fopIvXU56fT6TTVapUXXnihZvxTn/ZopfHIe69m65D9CHmP4eWQd8pWE5zb5WexU0HeTIh3u85W7ESQ8/k8N27cQCnF+Pj4uuh1q8qIZiKm3YinpmkN7Rw9TwMvosvn8zz//PO11uV2PHrvxwi5nWvX56eVUqTTaR555JF1xj/JZJJisVhLGW6sn96pyDZ7k9qP45vgAAjyVieZYRg7Slnk83kmJiawLIsTJ040nCrdLkHebh3PG3liYoJEIrGpE1w7Gl+2WqNQKHDz5k1s2+bUqVMNo42tNgV3e/G3SyzqPQ0sy8JxHC5evLhp63K9SG9m5biRe1H21g46OTwVGhv/bMxP11fa1Pt7eIMC2uXvkc/n75lfTCvse0Heiu0EOZfLMTExgeM4nDx5csuhoZ2OkOtN6uPx+LaWnO2YGtJIkEulEhMTE5RKJU6dOrUup7iRdtpvdrIOuf7Ru740zPPc9XLTU1NTOI6zruKgUUfcfoyQO8V2KYXt8tONhqfW1083m59WSnV0Enan2PeCvN2mnue2VU82m2ViYgKlFCdOnNhRrqldY5w2CnK9EMdisYZt4I1ox9SQekGuVCpMTEyQz+c5efIk/f39t79bKcFxoEGlyl4Xj+0EvtHop/qIzvNArp8oEovFqFarmKbZdgFtZ9nb3aLZHO9mU67rRz3V56d1XV8XTW/1NLOf9g02su8FeSs2RrX1E5xPnjy5qxxTu+qHvXW8+XkTExPEYrEdTwtp5/F4TS5vvPEGmUyGE6OHubC0gP67/xviyhXQA4h//Efo6cF9xzsgEoXTp3E//GGou4jawV7p1NssoqufeJ1Op6lUKqysrGAYxrqURywWazoy62TZW6dod1NIfX7acRyy2SyXL1/e9GkmEAjcsZEI25de7lUOhCBvdjGbpollWaRSqdoE5/vuu6+p3FK7UhaaplGpVHjuueeaEuL6dVpJF1iWxfLyMoVCgTPHjnH+H59G/3f/MyoURSwswuhhqBRRl85Adx/6q8+hurpQhRT6978Lp8/ivv+DTb//RvaKIG9Gfb7ZuxEePnwY27bXGQEVCoVafrRepHeyidjpHHIn6HTbtFfyttXTjCfU8/PzfPvb3+YrX/kK1WqVT3/601y4cIG3ve1tjIyMNH0cmUyGX/u1X+PKlSsIIfjTP/1TnnjiiZY/XyMOhCA3QilFLpdjdXUVYNMJzjulVUGunyjtOA6PPPJIU0Ls0WyDieM4TE9Pk0wm6erq4uj1Kxz+t/8jYmEONXoE1d+NSChkIowwBfR3IRZmYDCKGj2CWFtFhEKo1C30//23OVuqIiZ+AfWRj0KLEcleFuR66iPZzYyA6vOjyWTyDv9jL6Krb1rqZG66U9xLL+T6pxlv/+fs2bP83M/9HJ/4xCe4dOkSV65cYWhoqCVB/tjHPsZ73vMe/uqv/grLshqmQdvFgRDk+ujKy8lOTU0RCoWIRCI88MADLb+HZ5azW+qFOBKJcP/99/PKK6+0JMaw+wjZm7a9uLjI2NgYT1y6hPM7/wvxp/8GOTaOfPB+tFefR5u8inrgMlpmCQpp5OhlVF8XIp1Em3sd4t3I0SOIUgm6TEzTQf/Of4S/+Arue34G9W8+Dk1Eefvp8XI7gdsqP1r/2O3Ng/PKwizLIhgMtj1S3q9Ob82uXSgUGB4e5n3vex/ve9/7WjqGbDbL9773Pb70pS8B/1zF0ykOhCDD+rrdeDzO/fffTzgc5oc//GFb1t+tsbxSilQqxcTEBJFIhAsXLrR1JPlOc8hSSmZnZ5mbm6tZg+rLi5i/+d8QfvMK1aFDmKaNPvkC8qELqGgcbXoCdB114UG06ddur3PxcdTJE2hv/gh95kfIQ0dh4DCsuhCLwpF+jG99HfXtv8Z58r3w0d+A8M4/715PWWykmRtIo/l89ZuI8/PzlMtlXnrpJYB1tdOxWIxgMNjU++5XQW7FWKhdXXpTU1MMDAzwK7/yK7z66qtcvnyZz3/+8229lus5EIJDtBThAAAgAElEQVS8srLC9evX6erq2vUE552y05RFvRCHw+G2C7HHdhGylJL5+Xlu3brF8PBwzSxfzE9i/O7HoSdB5aFHCcxcQ0vZyAceRcxcQaQE8sIlqJYQFQd19gFEIYU+/TKqdwh5+RFQEu3NHyFWq+jRHuiNAwL+xVnES29ifvOv0P/pOzhP/CT2L30cEvuvhXUr2plaqH/sLhaLBAIBhoeH1xkwZbNZ5ufnqVartWqD+rTHdqK1X6eF7IW2acdxePnll/nCF77AY489xsc+9jGeeuopfvu3f7st62/kQAiyaZp3dLK1m+0iUs9wx/N22EqI66082308SikWFhaYnp5mcHBw3fgoMT+J+b/+OiKbQp6/TOjWa5ROnyI4cAjtzVegdwDV040++zqq/xCqOwxOGTl2DDF6BDF3FW3pGuroOdTF86BHCM9NIPQuVDCEiiSQ734cvvccLKwg/uHbGC//E5VzFyn9/K8TOXJq0wtsP0XId6MxpN6Aqd5G0uuG2+jWFgqF7uhE9Nbq9LSQVtujt1r7Xo9vGh0dZXR0lMceewyA97///Tz11FNtWbsRB0KQe3p6thXLVi+grX7fi4hDoRDnz5/fdvPQE9NWLpKNEXK9J3FfXx+PPPLIulzXOjG+8DDardeQkTgioqEvvYa8cA5lGIhcHnnfg4ilG4hKCnXqQbSVG6CbyAf/BaK4hpZ8E9k/BjEDbSCE6ktAuUxZgawWCPzURczXbmFMzeKWChhXXiJy6+Pkxo7zxgPvRg2fuMO9zfsM+4F76Ye8WTdcpVKpVXssLy9TKpVqJkCBQADbtrEsq+35z2YN5HdCKxHyVg1Nu2F4eJixsTHefPNNTp8+zdNPP825c+fasnYjDoQgb3USe+LXCV9dT4iDwSDnzp3bcRWHd0ytRBb19cxeq3W9J/E68muYf/Yp1Ikx3PAD6JOvouI9yK4E4WwSeew8Ij2FEKCOnoPiGvL0Q+BU0JfeQPYcglgIfe0KKjGEe+ERRLWKyC5RSAwTs1MYKo/oPkU00A9uCfHoMKpaRMtUQHPRpEvf/BQ9hf8b+8hxUg//LGviSK0CwXXdmljE4/G2GKd3kr3UOi2EIBwOEw6HGzZZrKysYFkWV69exbbtHU9x2QmdnqfXzFNvPp/nxIkTbTuOL3zhC3z4wx+uWSt88YtfbNvaG9m7Z3yb8Cw423lxe6mJ3QqxRzuaOoQQ6+qZN82d2xbmn/1bRCaJOn4BI3kFNdqP7D+EypfJRRLEUzchGEKNHENbvYHsO4LGMlDCffBtiFIWsTqDe+R+tMwEWr6AHD6NE6zgVnTsYB9acJBoYRblhHH7x5E9fejvCaH9v88jpY5wFeguQroE5yYZSf8Hhg4fxXr055D3P878/DzFYrE2AcV7FN+4sRUKhe55RcZ+aZ32mixc18VxnJph+1ZTXOrL8nbyXe/F/HS7rTcffPBBXnzxxbattxUHQpC3MxhqR0MH3D5Bnn/+eQKBQFNC7NGqIHvm8KVSiccff3zzEjqlMP76c2i3riEPnUKs3ESZQVR/L3p2Ajl8mmj2FurIwyjdQJu9gjx0GlGcAxTq8Bn09BuoSC9q/DSIADJwCmllMHMTWOFBIiFJWCsgE6dwewfQMtfRizdxE0dwh4/g/vdHML72d1CVKGUgKjaEdIQMoCVnCf2X/4B89f8jPvYYcvhhDh8+XHf4//wons/nWVxcpFKp3LGx1Up3XDN0Mod8NyLvraa4eLP5Nn7Xm01xaXaix07YC5t6d5sDIchb0apJPdxuufacz86fP7+lCdFOaFaQM5kMN2/exDAMzpw5w5tvvrllPbP26t8i8knk8HFEaQWUQo6eRF+bRA6NY+SmkLoJIRu9NIt74TJCOqjw8dtphvQEsvcYws2glReodp8gwCrl0AAycoJQ5gY2Ok7fSShNgx7AHruI5tro2UlUYBAnEqX6vseJfvm/ooZCqFAQFIhSBYQJJojcCoPX/obupR8gyj+Fe+rdoGmbPoo7jlOL8BYXFykWiw2j6U5aWXZq3U48/u8kFbLZbL76luVGU1xKpRLVanVXI592SrNiv1+9kOGACHKnImRPiE3T5MyZM9y4caMtGxi7FeR6T2Kv9VspteUaYvkGxgt/BpqBGu1DqS5UqA+xNovsO4oozoNmUE4MECstIfvH0QqTEIig+roRdhVn4FG08hqqCIXIMHFnHic6hGFIpDNDaewc+VyWHlGBnlNU3VWwpiB2lEroKKYIodsl5NhRcj//KLH/+BwiEUEOJJDhMErX0MoWQigI62jlPMbVv0Vf+AH22COoY+8F/c48u2EYDTe26i02FxcXKZfLVKtVrl+/vq4CoR0R3V7KIW9HK6Vpm7Use1NcVlZWWFhYYGpqCmjvFJdWxjf5EfIepRlB9kyIdF3nzJkzNRP0u21SX+9JPD4+vu4k2/Ikt0qYT/97hHSRI/fdjnQHxtEL11H9PahwBCkHkcIgsvIGsv8kojBzW4wTPWjVVZyecezyJHYwQik6QtyMYmnDuMUpkAZO90lsaxbCEdbiCTQkQY5iqxKOtYQw+ykGdCyjTMjoQ1x6GLGQJfTGNHpyDdkTR/V14XSFUSYIVyBKZWQsgKwU0We+h1r5Ec7wBRj7Vwh9682dRhab1WqVa9euMTAwQLFYrOWpN0693m3TxX7JIXu0W+jrp7jcunWLc+fOYRjGplNcPAOm3d4Um01Z5PP5fWlOD28BQd5NysJLCei6zunTp++YRnG3TOpLpRI3b96kUqlw6tSpXadIjH/8vxC5JHLkDFp6AhUbRJQXUbqJisXQyis4ff2I0hSZkWNEohGMyGmE5qIXZ6l2nUSWp6mKKDIaJqDyVOMDZKxZAtFToAfRyysQO4FlL6LJPDI6RtaZR9e7MGNnkXYeJUuI6FHW5DJCaBTe/zMMf/0/QTGDmSlhLK2iBrpQPTFk0AFTRxlh9GIJRADlVBDLryIz16j2n8EYfDdGYHfGULquN/Sa8Jzb6psudioc+z2H3E7qo++dTHGpvyluN8Wl2eOWUu7pCp2t2J9HvYHtUhbbmfDUC/FWbnDN+lk0WqdRhFzvSeyZw+/2AtXmnwc3h3v4HFpxEaUHUEEDrWwhB0+jFadxe05CcRIV6kWjgqNKVHoP4VTXqATHwa4QjxxG6mWQRWT8OFVrFi04RF7PI1UavXcUV1WwswMEIyaOu4AZOkJRpSiRxIgdoiQNogQwGaWoUpRFEvXexzn5f3yd8pFhLFNDWJLgcopqfwIZCGBIC6EpqmYYo2Kh44Ku0LLXqZSmcBLHCPe8i2CweftPIcSmTRdebtoTDqVUrfogHo8Ti8X2ZQ65UwK1k5tT/RSX+t/bboqL4zg4jrOr8lCl1L6pZ2/EgRBk2NqCc7MIOZPJMDExgRBiR7acu/Wz2IyNTm3VapXJycnbnsQnTnDu3LnmIqVqDuPHXwNVxu0fwYmHceP3o9kWgjGM3AQyOoSsLoIRxgqaGHYRJ34cx5qjoHrRomk0s4tVQ6CrbgL6SYSdRw+PUVCrCEwIDVOUSwQCh8n2r6ILCBv3IaWLIfsoaQ4FlgmZwyzrBVxsutQoApfk8DKhf/kEw//4MoR0KocGseNBbFNDc6pYehA9EMYsl9ACGhUjhFIaerWKoSmc4gz56v9DKn6IROxtxAKHWv57eDRybvOqD/L5PJlMhrm5OXK5XC1PWR/htSqm+yVl0Q62m+LizeN7/fXXdzTFxcPTgHtdGtksB0aQN6NReiCbzXLz5k2EEIyPj+/YH7ndOWTLspiamiKVSnH8+HHOnDnT0olkvPEXCLuI23caSlOoxFEcaxpC/VREGqK9YPYSlMMgDERxhjXVR8Saw9H70UIFhB7FMk1cmYfQGKtygWDoEDkydHESgYZtJwmEjpJWi+CEccNB1sQykcBhVsnTxyCm7CfLMkERx9FhUaSI0U+FYabfMUrXG7c3gSILSezuKKqvF0OAMBT5iIGuAgSkJFAqo4IGlUgQWwvcruDQFKKyyKr7TZKhfnqDD9MTONby36UR9dUHHm+++WZtoopXy1ssFm9/nga56Z2yFzf1tqPdwudtIiYSCebn57l06dKOprh437WUsmPGP3eDAyPIW0XInojWC/GpU6d2nfjf6dDU7fAsOZPJJMeOHWN8fLzpC9GLqrTkK+hLLyIjg8jSDBhRLDcDmoFtGuC4yMgYlr2AFTtGyZ2nIgZQwsYIn0EJiWYLbDOMI9MYoaMU5AJBc4QMqxhalJRZoUqZcPgwjrCJyZNkKyk04WAYw6xoK8TFIEmRR6IIcQgLSVAJAiLMip4lprpJm4Kn/9t38e4/+jaF3n5QFt1zixSGeqkEYyRKZQxdkekboKhrGLZNpGKDyFGJhLH02xeeaVtIscqi+gcW3B56Ahc4pI+v+246gVIK0zRJJBJ31PLWTxXxNrVM06ylO7aL7vZbhNyp77j+mHc6xeVv/uZv+PKXv0yxWOQ3f/M3uXjxIu9973sZHR1t+jhc1+Xhh2/Xx3/rW99q+XNtx4ER5M0wDGOdpWEzQuyh6zqVSqXpY/E8iefm5ggGgzzxxBNt8bMQykKb/y4qEMMNmIiqxI4PQmUe2XUKtzqDiB7HsueRWh9lew4looi4RErBasjCooCROISUVSKMYMkSQTVKhhUMLYZlGlhUCBlDrIkUCTHMlJFCF0E0o5uYHiQhj5JikbBIUNBgVeTopp95LUNUhQmrUSrCQgmJ03+C19/zEOd/dJ18vI+S6CeeTtNbWSE9MoAT0OlLp5GRANlEglUzjNJ04uUyUKAcDFExTFyhobsOjlhjQTzHrLpKr36KE+Js09/rdmwmQvX5z3rqo7uZmZladFf/CO4N9LxXdcjNrtup1MBOKiw2ft+f+MQnePLJJ/nc5z7HBz7wAV5//XXS6XRLgvz5z3+es2fPksvlml5jNxxoQc7lcty4cYNisci5c+daLoVpNmXhum7Nk3h0dJSLFy8yOzvb8kVSS32s/QOV8Ap631lsJ01Yu4xQFnr4DK6TQgR6KduLOMrEMstomoEKxVAyQ9VNICgQCoyRIUnEHGGOJGGtl6xWJM4YUployiEkelkTSRLaCCusEBU9rAXKCN3C0aKktBz98ih5HIKuQAjJkp6h1+1jSS+gizJRGSellRhxo8w99FOMX5tE16GvkCZ1uJtsKIFZtUnkMiz3dRNW0JPJUIrHWItHyMaiuJqBFAaBahUXcINBHAyQCuEWSIprzBkzxAPDdCqTuBsh2qwzzqs8SKVSzMzMkM/nee2113YUTe+GTgryXmybHhgY4O1vfztvf/vbWzqGubk5/vZv/5ZPfepT/N7v/V5La+2UAyPI9RdILpfj5s2bKKU4efIk165da0td4m4FWUrJ3Nwcs7OzjIyM8Pjjj2MYRq2zrFU0TcMuL1BJP4tmJCi5SYQeIGWkULi4Zhwbk4odwSROPNiNoRyECFCxZwkEj1AJLBI2D5FWS4T0ftKkCGpxCrqFEAZFDYoiS1T0syrSDKqT5JVDlxojpxURjo4izJrI08sAs0aaftnDvFFClxpxNUxZgx7Zy7JRoKJXiLsJrpkFevQI3/vpn+Ff/+VXWR09jHDg8Oo8qwND5OODmBoUNJOiFidhFRlMp8kkeiiGdIRycXWo6EFwFVBFiCBSN3GlBKfEmj5D8bxBQVc86J6hi+ZHeNXTjtRCoxKx5557jrNnz64T6lKpVNsAqxfq3VQe7MfcdCtt0+2qQf74xz/O7/7u75LP59uy3k44MIIMt4XYa+08depU27t1dirIUkoWFxeZnp5maGhonScxtHOCtUZ19duAQga7wEmiBQeQzgKaOYrNMrbVg4oVMI3DLJEkqg+TEili4gRVWUVlBiAaJixHKIkKOgGquo4rKhhaDzmRIy4GWdHS9DLELW2NXnqZFHmiIkrZDdKjQvSIIBmRY8DtY07PEizoFIKQ00oErRCrUZfRcg8YgqqQDLk9zBh57CPHuXr2fkbmb5EQNosjY0RKRXpUluTgCAFsErLCQt8IlhCYVpmuYppMtAebIGG3hKULKlqMijBRLpiAhcTVNDRcMizxnUCGkOzhYecUI7R2wXYq11vfcFGfK/Vc2wqFAqurq7WJy177cn003ei49qsg30tjoW9961sMDg5y+fJlnnnmmZbX2ykHRpDn5+eZm5vriBB7bCfISimWlpaYmppq6Em803V2SlS/hbTm0cNjlJwkRnCEoj2P6yaomkl00U05WiCgJciqFUwtSoYsJiFyWhmpKyo9GtlgESHiFHHoYuh2150K4lChWxxiSVuhl0EWxG0xXhR5EiJGVrhIU5AUUNSLRCtRbmlVRio9EDEIoFgRFrmQoqsY5GakSndGkIpoBKWiqxSnamp89yffyy9+7f9kqnuQIytLWJEQt3qGOLSWQkYCTHf30VfOoumShVg/FRHB1gyEUlRlCFNAtFrEwKEYiFLSTFwEmgs6LrYyUa5DTk/zn4MvE5BdPOCMcl4Nbv8lN6BTG1mbibzn2lYfTXuVB/l8vtbCXC6XazXWG3PTnRDOuzVxeje0S5C///3v881vfpO/+7u/o1KpkMvl+MhHPsJXvvKVltfeigMjyIcPH2Z4eLjh/9M0rS0nz1ZTOrx5ft3d3Vy+fHnLcqd2RMiOqmJ1r1DSTqEbAXAMcpZ1u8MtrIPQcUwD0HA1E0UZpUdwyWDovVgiTVQboBRME+d2BNzNIEtamn41wKSeZkj2MatnGXHGSAqXPjVKVbj0YbIqyhgYFJTE0R1EQWM5ZjPs9vDjWJExN8SEKDEmu9EkBEwYswU3E0XG3BjTegVbaaiq4EoowtjDP8lPzr7C1NgxFDr9uRUywRCWFuW+tSVW4j1kzC6Gimtkg0FK4T6CmkVQq3LL7EEnRrdjEaWIQpLXwzjCoCoElhIEcXElCE1Q0Ap8N3idf5LzXHCG+Qk5jNhltvle17nWVx709/fXXt84SHVqaop8Ps8bb7xRE3VvKECrn2GvpizGxsZafv/PfvazfPaznwXgmWee4XOf+1zHxRgOkCB7otsILyJt9eTZGNl65WsTExPE4/Edz/Nrx8W8WHmBcryEowYpmWu4xRhur0tMO0uWNL0cw8YmqEaQWITpo0yOuDjMilimSwyzIlbR82FWutP0MsCClqZf9TGnrTEge5nVMgzIbqaMIn0qzmuiTLcKkxKSmOpC2QryZXTNwOwKEpYGt7QSo7KLG1qJo06cG6LMCBGmpIuBIGx3kxcwJrpYFQ6BoCDuwF+OP8rjyTfQNcl91ioTQ0O4QlFVOqvGUUzX4kR2kVvxYZQSHC4ssRLtJSPiHHLzuIbOarALR4vjSEGEKiUlkSJAUANLV1SVAFdH12ykZlIWFX5gzvFDleSk1cfPMEJwB5dEp1IW7aDRINUXX3yR8fHxWmdc/USRjTamuxHBvThxej8bC8EBEuSt8Lr1dlOk34j6i9AzqQ+FQly8eHFLG8x2U3EzLFdfQdkBioE1DDeMHa8SEnFSYpWQiDGnpQiLOBmRJioSrIkicdHNKkUGOMqCcuhSR1nTc3TLGGVN0at6SYoCPSRY0gr0qDgLWpluFWVFVEmoEGnhEJIGKcdBUxp2LIrUNAJukDwO/aqPAoKjMkhRuBwnzjXKHFcRJqWFhiDlCspK0i/DTEibM1qAgG3yl8fewf/w429yo/sQCft2tPtGfJQhlUcGFM92jRNyLRwlmNfDHKoUORwoMR3oR6ExQJqsGSOrxclpAZQOjqXjaBpCQUiX2HoVW+jYjo4SCkNzqAKvmWu8KrOMOd38awboE5ufK500F+oE9e3fjaLpfD6/zlqzfj7fVtF0p6eFNHNN5XK5tgvyO9/5Tt75zne2dc3NeEsIcjtN6h3H4YUXXsA0zZZM6ptFSsmNtf+CMiVSBRF6GUOPo1hDaiGUqCA1E0QFV+ggNCwh0IROWUh0DDLCxRYua8KmkjBY1tXtf8ftdukMOt2yi7KAAanhIOhTLkXloNsOWU0S0gOU0cBRSFenqitMFWRJuQTdACnl0CsDzOEwkuthYhXi1TCVXpdYRJAOORQFBJ0ArytFv2Py5cRFfjrxGt2VHP0UuN51jLHSKjJoMG0McsJOUghGSendDOlp5kUPORkCx6Vfllh2E4SlTV8wxYrqwpZBYoEqjumQljFc18SyIRSwCOkVisrEUgEcqSFwcYXiup7hKVlgQIb5OTXAuH73brSdpJGgNoqm64cCeB7I5XJ5nVG9N2JrL6YscrncvnV6gwMkyNsZDLXaYefVNFuWxUMPPXSHo1WnUUrdrtxIvkbg+CJhbYBceA3T7SWvrxHXhlkRKbrEECsiRQ9DLIkUvQyyqKXpU/0siNspiUUtS4/sYUHkCVUDFKMuCRWmICqEVIi8sKlqigoSJTUcJanYoKSOqyXoVQEqNvRoBoVyhYgmIBCiKlwKroYFGMog4yjEcpAZodBsg6Vel/BiiNSwTfyFOPlhl+6cQbhbUY26xHWbPzj8Xr7wxh/xcvwYZwtLFIImS7KP+6rzzAd6KThhjopFrqsBdF1wMrjKnOhjWXQTM6tMV3qhDAmzTFcgS7IURzMF3ZE8BRWiqiKU3DBVKZCugR5w0AGJietqSKWQKOZFhd+XC3RVQrxXdPH24PoNtU5VWdxrthoKsHHadaVSwTRNXNdt+4itVlIW+9WcHg6QIG9Fffv0bvE8iR3H4dSpU1y7dq1tUfFOLux1Q0y7u7DuF1TEEYoqgFsNU9Q1omYfRU0QU6NUhSDBECWh6KafjKjQq3pZEGsMqD4WtAxDsp9pPcsht5eZWI5BO8GcWWRQdjErivSrOMuiStQNkVY2VBWYJkIzMREsSkUYnVnbJYrBiisYsQymbcGoFmDZcolPmKTTGmElCEYUCNAcnWoFRNHASkDZ0smFwcjoZMsawakw3xuO8mfmv+S0O8e0OUBBhblQneFWcJCypXNCLPFjNUqvUSWsZ5moHCJslOkK2cxVBxkIltFDFvPVPgQKC3Ack0pGozdapjeQI1ONoGQQPeggNUW1auBKDTSFIW6XzElXoJRkVa/ypzLFV/N5HiPCh0PRfZeyaAeNjOpnZmZqpXrtHrH1VhzfBAdIkNs9NWQzT2JvrVYmRsPOpmGvra1x48YNIpEIDz74IMvhJVZZo48BFrQ14rKLVKRIvwyxoKfpVb0saTm6VBerokhYhSkJA4WJUEOsKEWvOsw0Lj3uIVJKElmLUogajNpDlJAcJUxBOPSXQixTJaGC5EMCQxrYQEkKIhisSpdBgkxjccjVuSEd7iPMa5UqXS9EuXWxwmA+zJvHLQZvhJg/YjM4FWJxwKLvtRCVuCJsCRxAlAVml0R3NJYl/HnpCb544o94rTLK2a4l/qlyCtcOoCvFEn306UWiepHp0iFGw6uUCZIs9HE4liKrwqSyPQzHs5SFyXI1TixuEQ8qVrI9YAlcqYiGbCrlAG5VIxIqYxkGJTuAXQ1gI5AoDNO9nc6Qkiw2/0nl+c+5MoPhOP+TbTPWoKSxWfbyRuFmSCmJxWIMDAzc4dhWP2KrUCjc4X+8XTTdrCA7jtOw1HS/cGAEGbY2GCqXyztao1wuMzExQaFQaOhJ7FlwtirInrA3Oum89IimaZw/f55YLIaLy1Vew8QkRZ6wCpMOFQlbQRYCa/TJHha1LMOyjxkv+tVzDMtuZrQ8/TJOVlRYQ1EFVqVNGIOlmMmQG+BVqpwgxhuqwlDWZTZqckTFuSpsussBykqhSY1uYZB1JaOaQdZVjFahqARH1iLMLiliC3GqI5Kh16PkEpLuyRCFiCKQMsjZoPImVkxjJSrprRgku1x6qwYLlqKnouGuKBbX+vlG9DI/O/AyqWocw9I4NbjEldxhBiIFRFjyyuopYpEyb2aOIIVGfyxPphhDCZ2jPUmWS/3YSmesO0Wq3Eu1FGCwO0PeDlEqxZCGQhgKmYvhVEEPOsQjNhUEoiqwpUZVgbJcNCUwTQdLGdhCciMe4L/L5Ti8VuUj8RDv6G49z7wfBXmztMJOR2xVKpVNhwI0k7LYy08YO+VACfJm7CRCrlQqTE5Oks1mOXnyJOfPn990I6RTJvXFYpGbN29iWRb33XffusfDm7xJiRK9DJLUUkTpIqtlcJWGjk5eswkRZEkr0C0jzGo5hmSCGS3HmNvDhJZnTHYxJYoMyBhFqgglCDsaSc1l2A3yY1HiUEljOmYwTpQ3VIVDMsyydDClgY7GddtlTAvwvZLNBT3Ei1VF71SAVJdCd0zEMSigES/rLGouh7Im030uA1Mm+R6H4JRBWQiiGdArGr2rGoarcQyoFCGR1zAN+Isb7+Jf9b/CajbBmaFF3lw5zEg4T9CoMrUwyvjYAqvlLsygy+DYCrOLQxiGg6sEi1MnMQ2HYKxKaq6XeF8VJ14iv9pHMOQQ6ElTzHUjXZ1oX5aqHaSSi6AwkJaBKQWGpmG6GlZQYQsX19bQKyBtl5CmsJTilmvz71IuidUyT0ZC/JvhcNNVB50y6umkSO1GNDfzP95sKEC5XGZ2drZWN72bEVv77cZWz1tCkLfKIdd7Ep84cYKzZ892bGhqPfWCXD8pZHx8fF3bLECVKj/mGhGiLJOiS3WzrKXprnaxHCoyJPuZ1TL0y9utzkF0TAxSwqJbhZkReQ7LOJNagWNuF9dFkVEZ5xZlgq5AcyVLwuawCDEdsjlNjNdlhZMqzLR0iCkTECw7kqNagNeqNuPlEK+7DtHZADkDpK0TKmskexyGFwIs9Dn0LBmkDUUwr2NLQc7WOSQ01kxFoqBR0EEInZClUdUUCVfhOhqBgkBqcb51/W28/8x/ZS4zSIIqXZEsN+eOcXx0gWwhiiwEOXxsmYXpEbrjJUSXxerUMAPHVikpk/xCN5FTWZYXu3HngmimBMNArcSIjOWwlEl1KU4wYaP15amuxdAUVI7jNEAAACAASURBVBMOltKQ6TCipGFIjUjYxQ5LqroBFYHuajhKoStF1nX46lqZry6WOY/iNwZgfGB3G1ydmhbSyci7HVUWjYYCKKV47rnniEQiuxqxValU2jKE+F5yoAR5s5RFoyoL27aZnp5meXmZY8eOcd999+3oxG2nIFerVd58801SqRQnT57cdFLIs9oU83o33W6MVb1CTgaoaFGSpkIvh1gMC/rlYV6nwiFnjOuUGVI9zFMlpgJUlOKaEnQT5VnX4gT9vCgt+oshJnWNqNTRzSBXHZdRLc53rSpn9W5eshx6VJCUEqzZkmNGgO8WLYZnYzwfAr1kUikLkgmXvishbh6zSUyGWXIFWUcnuqaTDyviOQ0TQe8KBNMawxGFXhaEHIHSIVARdLvcHuekDHQJhiP4weo7eO+x56BgMjK2zNzCUY4PLlGVJhE7SvzwElZ5mLFDeaqmRVgb/v/Ze/MYS7PzvO93zvm2u99b+15d3VW9r7NzSIpWGGlkGhZEjZEoUaQookDBQBACRGIxjv8w5ERQIAuxAVlIKNiQo2gxAkmQLQWyFDkSKZIzPfv0XlVdXfu+3f3bzjn5o1jFnpnunt6GHLb8/FOoe+ueD99X53u+977v+zwv7tE1jMjSKTOsHV9HhhnKI5oNuYHf7iSylp18A7vYiQGUEbCZQWgJQ02SyEOtZ1BFTVhpIWoZdEuSWoHR4NUUJtUIV6AdAAE4aC3RruBSavjCoqRnqslnxSx/q9w+IJD9drG7eSF/P1lvwkcnDBFCoJSit7f3vkdsLS0tsby8TC73eIquCwsL/PRP/zRra2sIIfjiF7/Il770pUc9tQ/FE0XId8PtJJqmKXNzc6yurjIyMvLAnsSPg5DTNKVer7OxscGRI0fu+TDYpcUbzgIdNs+c22DQlJl16gzpMutOnULsEiPYIMXDY4oWfWSZFG3GTYFrtBi0WXZI2NSWCj6XTURvXXMr6zMcClYcSaAFFeFxJU44qbK8EyWMCI+qgWpqGcHnzVpC50yWzbzFpJZSw2G+rCnN+0Q9YCMHrynZzhn6NxVuIuiOBYWmQmvo1gIRg2hCYBU2BqXBTQUyASfW9BSgqwRDg5qjJyXyyEsUk3cInVN0lzXW9uFKnzSzhRYVHK9FQ4QUGaBm1vBkDoXPNpuU004aok2TGn2mi51sAysUI7bI2kgDrEPF5FiRIbF1qCQlqsKgChKv5pJJBNXOECEMTtVHBZZmRwhthWiBjCWeAS+G0NHEjiRjHbQSVH2X305H+bfbihcaKf9Z7za7u9+ZLLLvN7H/lfyjHHD6cVPTPSzuNWJrdXWVb3zjG9y4cYMLFy7Q1dXFr/zKr3DhwoWHOpbjOPzqr/4qTz31FPV6naeffpof+qEf4uTJk4/rdO583I909e8y7rahXdcljmNmZ2dZWlpiaGiIF1544aE206P4UBhjDnyRfd/n6NGj9Pf33/Mz33BuYoQlsRbPOqyJNhWTYVbU6E/yzGcjDukCU7JBr86hgA2r6SPDDZpM2DxXCDmks8ybkFZs6ZIOi1nFKZHhXSemP9lLH6xrwzEV8FYUc1wGbKWQ0xJ/SbKwBf31LKkD2ZogU5OEKXTsSNxNh7Bh6ZWCoCERDcjFAr8t0BJECsW2RGFxYomfgEoFBaC3YBk/YTh6so11r3P+/Nn3XjN7mtn6myjRpqpqZNQANbGBdcoI4ZLYmDxDNIlxGEYiiWhTMt2ENNFOQpfpZktto2x2ryPF2SFvCggUq2qHsimhESx5NcpOHnzLakeLnA7osjlWE00eyDRc8g3BlhsRBxFu3UcKST2X7nVjtCDfFEQCUgFGQhvLXzQdvna9j3FngJ84LPjhCWi3m+9xb4vjmDRNmZmZOSDqx9HT+1Gq6T6qtR/k4bQ/Yuuzn/0s+XyeYrHIV7/6VTY2Nh4pfdHf339wbxYKBU6cOMHS0tJ/JORHxb4ncb1ep6+v76GJeB8PEyHvizpu3bpFb28vzz//PAsLCx9acFkTNa6pFfpNmXlZZ1CXmVU1siaDEinbKiUfCm56dQ6ZIpOixSFT4BZtlFV0WJ9lkzAWuWzETQaMh8kGiNSlZAX1FEYaiiYKQUCPULzRTBl2CrwTWtp1SW7aYWEgpSNyUEqwlDH0rTqYAJqOpbzsoHMGtKS4qXB9KK4KHGORBpxI4mmBowV5C/1lw8RRwwufMQyPfedcw9AwOfnBayCFQ4f/NBvh18ipPkK9hVSKQPtsOdtkRQ87YotYOmSFx7qzS8F20pQRNeGTqeXZKkgC2wdWYkjp0RW0MKypFkO6yJZs00JyyORZESExLqMmw5qMWbOaXjfDVodmq5TQZQKCekLbdyg7AhqCXFNRx1INNBiB01akxiK0wNEgUkGI4WoM/8vbkv/jDcFzlQI/9VyBiW9PnGo0GszMzFAoFA7EF/s9vftR9L1SHnfDR5my+Kii74dtedvd3T3o7Lhd1PKomJ2d5a233uL5559/bGveDU8sIRtjWF5eZm5ujt7eXnK5HGNjYx/+wQ+B4zjvmRh9L9wu6qhUKu+x47yfSPtrzhTKShpoOk2OhtAMp520sQzoPA2jqdXb9BVLbBnLoO3iZqrpoJNrSUo2hXaiuSwcjqsiX0tSDtc9qtqynVgmXI83Y8GAFuBI3mlrTgc+kzVNuCnJzzssj6aUqgq/LdlxDBPzLlILxKagW4HTBrOjcAKFigSZKohU48bgx4KcDekr1zh2fofzL0Cx+B23MW5zWLtb/h+g6J1mJ3oToSO0isgzQM2ukTOdpLKJtillW2FTblLUFRLZJrYJPWmZlWKdDB6pSFlWbXp1hS0Z0RaCLt3FTRHSmZYpI0mwdNkCUsCmiClbh5yARdmkU2fJSJcFQhwHDrkOC6WUOCfpsg5ZLdiNBJVAIKqWsGUJU9gINKkEEUpIBBjBlrb8v6uGv/4DyYgSvDgMP3x+b291d3e/h0xuz5suLi4e5E1vt9gsFAp3bcP8qCdOfxRplo+TKKTRaPDyyy/zz/7ZP7vvYciPgieKkPdv6n1z+K6urgMSXF9ffyzHuN+2t31RRy6Xu6MLnFLqnnLua+xyUVv67SBvijbDJseCDQlw8JAs64Rxm+VqVnA4dVgwCUJbSri8oWOGmylzvktF+QxIxaU44ZwTcCVOKVrFkOPwRith3MCGgUZkOa095qfBu+GTsQKRt3TPeOSaDjtZTdF4eA2JAFLH4rcE2RBMBLmGRIQGNzH05CUnj8GLPxhyaEICJdI0R71ePzCyabfbB1XzQqFwMDH4TpBC0eE/y3r4/5FX/bT0Bo7ycQ00ZZMKfezYTTImhxSamm3RbXvYcHbxYxffFWw4DYbTCuvOXu64X2eYU1VKukBLJqyJhH5dZF0ktBAM6CxzxPipyyBZWhh84zBhXTbTKi2rGZUOS45hNU3oVS79vmBJJPi+Q8kKohicGIqRJahZmnWDsdDCYlCgYa5tWbss+eM38vSqMX5kUfDDf8uyr224W9601WpRr9fZ2tpidnb2wLD+9qkimUzm+3LA6cfF6S1JEl5++WV+8id/kh//8R9/bOveC08UIVerVd599907ehILIR7L5twXhtwNtVqNyclJHMc5EHXcCfcamGqw/JFcQqK4RciwzTBDiwkKXKdFn86QxzJDTG9DM5kNOUqOKRuTRJpebZgJXE7IDFMmxU8tRx2fS1HCKSegkQKJ5ClcNpop9Zogs57hL60haEj6XMl6xuBYSVdLkTiCfEvR0VDIxOLGe0lSJ5F4CTitlIJocv4kfP6/ylLpMmitMUZirT3oINgf766UQghBkiQHxLK5uUmtVuP1118/MLDZJxelFEXvBNvRG6BbGJmQo5uqXadoemjJbZSVZKzPltyly/awK3dwrIubwG5Qpy/tYFvVkdahbHwWnRp9ukBTxuxiGNMFFlQTpT0GrMuMbNJrMiTKck23GLFZVkhZ09CZuoSpZDK2HBE+1lgSKyghyTmCtoBmauj2FaGFJhrVBdkOwU7LoiJBLjWU6pDuCmTDkCKYb2X4v76p+MO/FIwVLc+cNvzgDxneb1J4p2Gq1lqiKDoQXuw/9PY7DpaXl+/YKvZxxKMYC93NE/1BYa3lC1/4AidOnODLX/7yY1nzfvBEEXImk+HChQsEQfCB9/Zzv48qq7xbDrnZbDI1NUWapkxMTHyo49S9Iu3XxRaLosWYKTBFi6a1VOxeB8W4zXKVkCNkmSdmx1Ucsj6XdMhQPaWeCSg4Wc4aRT0UDKc+7VTwTt0y4mb4WtOirGDEU1yqadxdj8ySYqpsyMeSzoYkFDC85eBEAi+UaGEgdZApFFOJCgVuCAU0vZV1LvzQKj/yd/eKccZoYK9taf+m2o98tdYHBL3/cNwnie7ubq5du8aZM2dot9sHaq592W02m0X2nKBRWcSTg1RljGSMREikyJIRAZqIou3HYvBMlrwJ2HKrdKdlGrKJBbpNwLxTpU+XaIiIUBhGdYFbqk5JZxECFkSTI7rAmoyJjOS4DJg2IVlcjjgO1/OWAQSHfMGNKGJIeETA9UgziIs1gum2pdNCQUjaqSUjwbHg+5A6EIUG6wtM0ZK2BU7bELQTijqH2JbMVWHxrxV/8ucOg4Hl5DHNJ/+OobP3jlvmPeOfbrfYXFtbY2trC631B1rFbo+mP05y4+/1+CbYmxjyW7/1W5w5c4bz588D8Eu/9Et87nOfeyzr3w1PFCH7vn/XCPijIuQwDJmenqbZbB5Ire93nTtF2gmGPxZLdFqfKZoc/nZUPEqWFpZVkzJhs7QtjKZ5lnaqLOuUXjfgYuRwLPV5NzbsJnDCc3m3lVISkn7X4fV6yrDrkEXwxqamvO7gbwhIYLzmoHYlKhB4LthQ4BrwQ4GMFflUIFqCvJAMd4aMnp/mqU9Juru7mZ01RFGE67oIIT6QV9z/n9z+v9kn6f2v3zdv3iSXywEcuI319vYepKHCMKTeqLEmF6nbHdquwW1maZRScnGRql8DPHwEGyqhN61ww6nht4sIx2FHBPTrAtMiojPpo4bGEtBpXJpCM5h2YAQkWCZMjlAYOlIfH8UGmlHrEwrLsokZDRM2sgppJKc8l2txShnFMV9xPYrpES4TGclkOwXr0OlLplqGrFZ0SMFiy+ImkiEFNhVoDWXXQGpxchavoDFtgYgFnhbsVuGVBYeL/6ug0zf0lS3HTxlO/7DB/ZDtvK+Qu32Kxv41v33i9b5f+O2tePeaKvJR9zd/r3PIn/rUp74nUuwnipDvVWDYN6l/VOwT6e0Kv3tJre+GuxX1/oo1Uiw9OktAhjB1OGw6mEsMGZPncpSSsYpCapi0MBr6bGdyxInglO/yditlSDkUXMFrjYQTvktDw1RT84nApboiqc1JhtoCpy1p5i0ilTgNQZARpC1LX1Wikr1CVIAgm0B/XnD+U20GTlzGDxQTExMEQUCSJARBwLvvvntgKl4sFg9SDr7v8/LRr9z1Ovzyn3yB7e3tg4eZMeYggt7/CXsPW8/r4og4ww3vDTpNF9v5XfwkS0IbYw1+TVOtNCg3Mmxmq/jaQVlDVUaMpGVmVZ28zlKTMZsiZUgXuKaaVEyGWKZsWs2IyXHdRnSkPiBYsCnjJssVk+Bohy4RcFUmTEQBTWNZ1XBM+OxokAjOCkXbCrCC855LW1uS1HIuK9mIQSeWw3mYqRu2gY6MpBpDOxZ0uIJ2ajGhoCQhcCBJwMtAMWtwewXNCJZTwerbiq9/3aGzbBgagsExzfA5i/8+V9g7EeftKY/9r/h3S3nc7ty23+XxsF4T94uPU1Hvu40nipDvhcelsLPW0mg0eO211x5I4fd+3ImQ61bzr9oNukWFf69jTooM13RMwUIOh9fjhBNGMalTIi056blc8gXHhcuOtFxqJ5zzfW6Fhl4h+YTn0ookjR3LcENxdVPQspZKU+FbQd23FNYUpcQi2wI3EXiOQrUhSAVFA6fG4YdfDmml0zQaDY4ePUqxWDwgS8dxOH78+MG12c8J7+zs8PMv/tMPvQ5f+Tv/8gOv/f7kL7/nZr+dnPvtIWbtNRLbAmspEbDu1ejRnWyUauR0FuNrjNDk6ortsqFUdVjLV/FTB88aVtyEQ2mRWdWgUwcgDDskHLEFpmSTXh2glWFVa06IDDdkSMW4KCWY1hGjYcJSRiGtpFs5vBqlHBYuK9qyEhmOOy6TIZBY+h3FO3VDvxD4QnCjBic8RaeFjTr0BFBBkGgIpEU5ewScE3vFUj+wyBRSLZDCYjRoK/CzIBxYjSXbM3DlusL/Y0s5bylXLJ29lu4xQ1q0qMyHR7J3S3nc7tx2e8rD932iKGJra4tCofBYUx4POy3k+90LGUA8YFj+sbZT2p/EeyfcvHmTfD7/Hinmg2Bf1LGwsECapvzAD/zAI31lC8OQK1eu8PTTTx+89hvxOv8u3aXTukgkizrhpMxwKYkppw4mjlmWLqeUx83UYI2gs9mGTIlcqrBa8M6OwEklRSWZrBm6jSS3pNhSFmNhcEvhtAVOTZB6FjdWqMhSNgoVQRAKenLwiU8aPvv3NEtLs6ytrXH48GF6enoOyPFOqYl93CsifhT8/uQvA7DAFFe4SIFuNuU2riiSYmhIQ8kUWXMbdCYVVt06InSQvktdGkrtgJVsQn5XUs0JMA5Z47DqGkbSPDMqoqR9DIJlYxizGW6YiC7rEwOrqWWcgMtJRA8+1grmY80x6XMtMWSNoojkaltzXLmsJFCNBEdcxdt1S4+QBEJwvQZnA0ktFDRbcCwjWdgxeIllOOeyti3oUIKChO0dQZcjCCw0dwVlD1wtSBuQUwInBRGBDzh67z3XWpxU4KSWuNkm61v6BgPKfVAZNXSfNBQGH/5WNsYcpDrK5TL1ev09KY/9aPphB6nevHmTcrl83+m/fXz2s5/lr/7qrz6ufhb3dSGeqAj5o5gaYq1leXmZ2dnZA2HJxYsXHzl/9v4IednE/Em6y3GR4ZKJGEHRKVwuJxEjbc2kIxl1As4IjzARDMYOW6Hg6zs+T+c9pkLLWmg5nXXYtpbrVUPflsLdlogYBkOFigVeW2Ik4EBnXeK2QYZQkpLxAcvn/p5h4oJlaWmJN96YY3Bw8KAhXmt9QMR3utYfFRG/f33hwH/+Z8doyCW8wQw5PNZUlR7TxaqzS1kXqKsGQkPWSrZUzEBSZiHToCvN0S5qJJZO47IQJPTXHZaCBkEkMMay7UmOJD7zbsSQ9TACGtpyWngs2IT+Vkw271NNLU+5Pmup4ahUWCmpJpZP+C67BoalZDQjqMXwfE7STgU2EXymAM0UjvgCrUClcCRISAXkpUO+JJAafA2ZvCUrgBgyBcgoiBtQKICDJalJcnmLbgusBuVbmk3wlUUYQYwgiRXRrGLpFoivK1xh8RXkOizFIUux39JzxtBx1CDvIwshpcT3fXK5HOPj48B3gqF6vX4w8brVaj2UWf3DpiziOL5jQf/7CU8UIcODGQzdC9Za1tfXuXnzJh0dHe8RdTwOvJ+QfzPZJEAyo2OOS5+lNKWjplGxYZciI9LntZolw16HxFt1Q48SjNuIt+uKLqk4l1csNCy9C4r8vMRLJY2sRSYCFQpykcBJBEFLICOBlwrKyjA6ssHPfaWHbB42Nzd55ZWpg3NWSh3kcb9XRPx+2BS++c83GPupfhpTIX73Gq2aRRXXSBCMHPVoCEVRFagFhnwSsEiCTbpoGsW2SOnUAVMyptIqMO9o4khQsg7XMByuK15ThkITqtawKxxGEsF/UIJx6zFvJKauGJAO/75tOOt4vBVZfCOoSMXFpuVC4HClYSlYSU4KvlG3PJuTXKtCD5CXgus7cKEomdrZO3ZGWOZWJSfLsLgJnUqQkTC7LThcsaxVBZ3+3k27sSPoLcFWG7oVuI5FpOC74GRBG4ErLTaxxKHEzUK4C64ShKGg7UBz1bK1Co60vPNvHFwPHA9KA4buM4bKYUv3aY13h87N9+eQhRD4vo/v+x9IeewPUn1/18ztCsTb762/qV7I8AQS8t3gui6tVuu+/nZra4vp6WlyuRxPPfXUHZ+6j+ooJaU82ESXkzbrqWYkzbMewut1TT6SvC7zHHMVoRZMtw3nsw4rkeWdhuZc1mUpNGwYl09lHFQsmb0sya4JZFMhMpZmxlKuSQpNgYoETiTIaImKYLgAn/kxw1P/SZPp6WW0zfDGG3v902fPniUIAowxB74C3+30xIdh4f/ZYfgfHiMYBtEdYK/U8S500vzmNstFQ+3dOu5hSLcMurqNOFxm1GSYdFqMmDy3nJCMcWlKTd1qDokM10XMMR1wy0upGIWfkSxqwwnr8q7UHA41K8JgrKUzbXNN+pyTcD2FLqWwEmYizfN5h1cbmuOBZDW2rMWWp4qSV6qa54qSqfpeJD5cgbd2DBc6JNfWFUNuSqlkmWkIJnosO7vQ5cN4757AZKzbIiOBMqB88CRIDTaBRlPiWotOIa0L8hnYrkLggRIC4Vr8DkHasKg8tHYkfgDxrqDYZTAeGCNII8vu64r5iw7ZDgPWRWgIitBzXtNzTtN10qKd+yPNO41+2jcE2q81LCwsEMcxnudRKBRoNpvEcfxQ99j3sxcyPIGEfK8I+cOKetVqlampKRzH4fTp0wdtWO/H/Yxful9oa/nFjQYt43Mr0hyJQppuhpbr8Yzr8GZT06sczmYc3mxoTvoOo4EkaQoKuy7dzYSlpstOHUo7kooB4VryW4JiKnFjiRcLCim4LcGhAfjR/9Jw7Jn9c07Z3d3l2rVrTExMvKdg93Ek4n3YxDL36/Mc+5+PsnVxl9LzHdQm6xROFYiqCa4vUDmH9qUtMi90U7+4wa0LlnSuzUzQxhQDBv0M0yLkmMlxTYYMG59NmeAYQYeUTJmUk8LnCgljwmUnsIhU0B1HzAUB54zgUgrdaUzLCGra4Qia1yPB+QBuxFBWknxGMN00/GBFsRjCuSwII3BiGCoLkggu+BHrDZeRrGApFOy0JVkHbi7C4U7L1LzkaK9lfk0wXLLUE9B1cPOwGwq6OgymCYUMiIzFRAJPSdJIkbQVu1YiLeg2lIqWTJdBakgTqO1IMnnL7rqge9Ti91laK9DclXg5S9LcEyvd/DOHmT9zaG8KMv3dWDpYvuDRfdbQc1ZTOWIR95HJ2zcEuv3+2k957E+6XlpaYnp6+qAj5Pae6Ts9CKIo+lj1Uj8snjhCvhvu1fb2oKKOe41felD8Yb3F1TilN0oYUA5TbpaznsdspLnc0jydcanFArcteSFxmV8XzDRhoqDItGB+LY/ThNFNh0AALQFCIAyUaoIghVwiODEOn/95Q8+321HTNGV2dpbV1VVc1+WZZ555T0R8txz595qIb8fS7y4z+t+OkhsKMLGBVoJTKtD45jaZF7upvrFN9qkK8UKTYCRDmhpkLUIeKtL+1jpzLzjod7aZOpyg65qlRhU9UOKYm+OyiTkpAyaJ6DUusTK0UsOgttzI+JwTiunUMK4c3IxLOxVMGEk1NjwTpmw0YSBK2Uhd0sRlQAm+seHwfAne2pGcCgQLLYFvoOwIlncCJgoJr6/DhS6YWbOMeOBlBRstQVevZXFXcGTYENcFoz2GpCHxpGVpTSIzsLQoCUYNi9OKkVHNek3Q3Z3iuYpcXiBSqDYEqRGsTgt6DlmSBEq9BiwIBNUVSaZsiY2g3G9AC9K6YOmKovdUiuOCk8DKGxnywzHrVyVrlxRb/8gn2hVM/GiCm4Xu03sk3XXa4N5Hje32lIfrupw+fRohBFrrO87ny2az73HFq9VqH3rffj/gbwwh3ylCflhRx+Ma41TThn+6ucMxY7nm+IwqxVEhqMeWMe0TxZL/MGc4nnVIhODmrqHLEZzMSJbmIJiWDMSCvCOQscRi8bUgWxW4KZSl5KkLmh/9oiX3bV8Ua/cKdnNzcwwNDfHMM8/w2muvsbGxcZDL+zjkie8HNrbM/+/zHP3HE2xd3KX4fAfV6zUKZ4u0tyL8TgchLXq9TfB0F+G3tghe6KX5zhb+uQ7itRZO2cO4ErW0i73Qh/76CtcHC+jFkKsIkhgaoWXsuSP01mM2vcyeRWnbkrGKeQvrIUx4kq834dlA8WrbZcKRLEkQCsoeTNcEp3Ih36pmOO3WuNrOM6o0LeOwHUs6CynTDZdT/ZYr6/DsgCVqS476lmZDkAeWYmhtSppNQaogjcEDnIKl2oRMhyVOLYfHNZ6AjpyFWLA+6+FPGDYXJPmSxUhD33GBAqrzCh1b8hVLqAUdQxppYHNHYrWk0GtReUPnhCVpC9DQqgo6TrcxbUnSFsQ1QbbXku2wbF9XuFnL1nXBpd902bgsqYwbxl5KyXZB9xlNzzlDtuvuOd/bUxVKqQ+kPPbbKxuNBjs7O/zBH/wBv/3bv02SJPzCL/wC58+f56WXXjoYTPyg+NM//VO+9KUvobXm537u5/jKV757e/+JanuDvcjvToKLNE158803ee6554jjmJmZGXZ2djhy5Ajd3d0PlHu6fPkyw8PDD/1ErtfrTE5O8i+Vz5uVTkaETzZVzNUFSzXBiK+4tmspSMGRrGSuYWm1LWczinhG0pqUpC7khUS1LEEiyVhwawLfSLoCy4ufMfzIfw23B7qbm5tMTe0V7MbGxg5SL+vr61SrVer1OmmaHnhJFItFvviJX3moc/xuQQaSF7/xAja1iO6A5vUGwdkOdr+1TeYT3VS/tYNzpEDrVgsrJGEkSVqG1HNJGgbTmSNej0iO95CutNGHKqQ1De2UpLuIc22d8NQgzpuLtE4PIyc3SfpK6IZmqK/EbGg54zu8Urc8GyheaxjGXclSbJGpICcEc204kxG8vS14sSh4fVtwLmtZa8FgmuDrFNoamTokrQxFV7Kw4XGqz3J1VnJuyHLlluTssOHGLcmJIcvUjOTEiCWuQnfO0t6WZDy4eVVx6LBhfU7S0Wlobsd4yqW3yUwVvQAAIABJREFUG2xT4EjYmJF4ARQ7DMvXFOPnNVLD4usOPUc0OhLszguGz2tIYeUthfKga9ygpGXnuiKJNcWhlEzWwcSCldcV5SOG4oBBKVh/V9FckfQ+leLlwRqI6wKEJa5Lkib0nDUMfTqlNGLpPqMpH7EIARcvXuS55557oH3w+uuv89WvfpWf+Zmf4e233+bll18+6AB5EGitOXr0KH/+53/O0NAQzz77LL/7u7/7OHyQ/+a1vd0L++5q09PTrK2tcejQIY4dO/ZQRYCHFZm0222mp6dpt9uY4QneXmxT2snxdluwEVqeLjhILO9uG84WFO0U1hqGs9YhWRRsLShCsScc6GgK/F1BYC1OvFesGyhY/tOXNS+8T25fr9e5ceMGruty7ty5A2e1fRXX7Wbc+9FHrVb72JMxgAkN0//bHB0/2k/7nRDRlWX5L+rIoQ7Wrlno7yb182hnF3uii/TVNewnB0hfW8N+ug89uYt9uhPTtqiSj3YV3to24alB/NeXiC4M4V1eIT7Zi7NWw3YEIAR+rcFsJUfmyhJvnhyleH2R18cHORK4bKYWV0ApAzfrlheKiu0I/nZZ0AgFL2VgatNhVMJ606WkBHGUQqIo+palqqKn1Obaqk9/Z53Ly3nG+kPmNj0ujGvStuTMsGVxStLXY7k5qeioWHZXodhlaEWQrRjKZYOpaopFh+VJh2wesllLsykYOKYRIVRKlqQh2Lgh8UoWN2fxPEuUVSRNQWtLIDzoPW6wsWXzhqK9K+g628bzFPV5ye5NRedxTWHQkDYF23OSuC4Y+UxK3Pw2GTfAK1kWv67I91k6ju31s0/+oUttUVA5bHjp10Mq4w8X8+3u7jIwMMBLL73ESy+99ND76eLFi4yPj3P48GEAfuInfoI/+qM/+siN6ffxxBHynQjWGMP8/DzNZhPXdR94bNP78aCEnCQJMzMzBxLhjs5O/valNu0o4VILTgaCSlbyyq7mhKc4WpRkIsnWkqC3qthZEdT1Xv/twK7E7uyJAvxUotqG0c6Uz39BcfwT7z3ufkqm1Wpx9OhRCoXChxbshBD89IV/8tDX5nuBtd9fxf/yeWxsoDOLmKzB4Qq8uo56rkLyyjrOc/3E72yinuoiWayjxoqk7QSlLGnWwZ1cJzk3iPvaMslTg7iXVknO9KKWq9jeHEIbvCikNdJN5tIKzVPD5N9epHF6mOzUCuHhLvzZdVbrEToR2BAWMwXytZA3Dh3hEx2Cr60Jnq8IXtmE43mYq0J/BuqhQVmNF0jqkaJYsVRrAceGQMVZ+ryE6oaknCRMX3HI+jFppHBzglpDQLC3N4pl6MjB5qykUrbcuuwQ5BKaDUmcCgb7NCKCwcOa5qZg9bpk6JShvi3oOmLwXUt9SbIzK+k/ZdDpXq+yjSGNoLEqcTOWjjFD2BY0Nl1qy5KRH0zRbUiagtqCpDhkcAJB3BQ4gUVIS3NNsf6OoHTIUJkw6FDQXJW0twUvfiXm7BcShHh4j4zHJZteWlp6j+/H0NAQr7766iOve7944gj5drxf1JHL5RgdHX3kdT/MgnMfWmvm5+dZXl5mdHT0QGb9r1Zi3mlo8kbxXA7ebVieCRR/11e0thRLG9BlBMGaZKcNTgiDsSStCjy1N/rIrwsODVqe/pEFTj6ffY+peZqm3Lp1i42NDcbHx+nq6vq+K9g9CGxbs/sbU3T+j2dovbKJ/3wPrUvbeBc6iZcaeEeLJI0YVXDQUqC2mphzfchXV7DPDiJfX8Oc70NMb2FPdiE2m4iuACyoZkQ80YP/1hLh2WEyry2QdBbxvnWLVLrIb8zTyBaoLQmcOEurd5Di4irNw0NUpueojh+mMnWLb5lRCguLXEyHyK2sc6XSxeGyz3rLkDUpTsah25FUchZagoaEjTlJ4IJuK1wFUgjcPLhKESWCSi5CGk3FDdm8Vaarp82VGwX6BhI21xxUAH4mIh94dJY06zck1kLPsGXu22ScyRiaNYfUARMJ1mclh55OyWRg6RUHqaDrqCYJoVCxNFYlGEu0K8kULB0jhrQJQkLSgEzBUpuVFEcMTmBBwsLXHKSEoU+mCCVIGoL2lqAyYfix/zuiMPCdqPjj4oX8vcITR8j7bW/7oo7Ozs4DUcfa2tpjmUj7YUW92x8E/f397xkbtRYb/vGtkGfzip2dCGdb8enYxe4IJncho6FnR6K3BHIXKo5AtCRSC3oMeE0YH4Uf/aJm9CTcvPmdnPn7C3a3K+z2r833S8HuQVH71zcp//xRvNEsNjYoxyI8BStN5DO98Mo66rl+9OvrqKd60de2kOe6SdeayNECJkxxpCXJOLiT28RjHbivLZDmAsyf36JRLhJ/bY36oRGoxti+Aol0cXeb1Esd5OfX2B4donxjjp0jh+i4Psvu0TFKU3PsHB6htLBCc6ifzMYW7a4KmY1t1hfauE1NIrIYUWBeSFpdFRy511ssA9CpIHXAl5ZmDMNlQyBgOCeYvJLhyJhmcibP+BHNykyBUndKFBsyuSaBiFm/3oEzEFFtObRCychxQ3tHMH7aQAoz33TpGDKowBJVBWNPa4QVLFxUGAtDZ1IcCSsXHbKdlo5DBhNbhIH6LZfOCYOQ4LiW1csO+X5L+YjBzVl2pyW7M4qg09B7fi83nbYhaQle/J9ijv7YB++hRzEW2k8zPAoGBwdZWFg4+H1xcZHBwcFHXvd+8cQRcrPZ5K233iKfz39A1PG4+ocdx6Hdbn/gdWstm5ubTE9Pf2Bk0z7+xVTCJ6zHW+9CnxOQyyrWGoIwhP6qRC4L3F2J8QXCQq6617aWiWDiCPzY3zcM3FarkFJijGFjY4Pp6ekHUtjBk0HGALalqf7GFB2/cJrWq5v4z/XQfGcL76lO4tka7ukK8XaIM5gjjTRKWkzgIG6towsZ0rktknyW6PoyzYkBuNoiOjEBaw3MsYA0AZlJsEoRhG3qg73kJ5eojo9QuTzH9sQYnddm2Tp2iNLUAjsTIxQXVqiP7pFw6kpK0/M4qcLZ0OAXEW4JkU8xeJDEKOuwtbGNsA7CWKQGhODcWJGMFbguTE06HBm2XLqhOHE05fp1xdhhzfKyZGRMkxOwdMOnNOQyd6lIvruJ1h6NumLg8A61JYdwO4MaiNiYzFPo1ZT7Lem2JN0RiJJl9brCy1v6j2ra64L5dxSFXkvXMY0UMPtNB69k6TyW4mYEu9cV9SVB+bClckSTxrD2hqK9JRl8McWkkIaCtC3oPqP5gX8SEdwlmP1eO709++yzTE1NcevWLQYHB/m93/s9fud3fueR171fPHGE7Pv+XUUd+73Ij4OQ3x8hV6tVJicn8X3/jiObAP54zvBv3hV0OIILnYKlXc3MlmRiV2AWJKIuMa7AeFDeAS8W5LTg+Ljh8/+dpXv4A0uSJAlLS0sUi8UPFOz+JhDx7aj+5k1KP38UbySHjTRuRoCSsB1iXEV8qYrOBbS3a8QDHSR/sUN0bgJubpOeH4StENPnopHIggcW3DCm1Vchc2WJ+rFhCpfmqZ0cpXRpnuqJUQrXFqifHKYws0J9fJDs6iZhT5nSzBJBI6G4sQxuAfwS0s9hcllMqwFegNOskwYF3FYd7RcQ7SbWzeK0ajj1Nm4Irs0yU/VRjV1EphdRneV6OsapU5prVxVnThucRKBykO5KbsxKDp/Q3LyiqAykSJ3QUfTprhhWrlcQAvqOahbeyTN4qolIU+a+UcIvJBQHI9anM/SOR0irqC1KNicVnROajmFD9ZZke0qR7zf4gzW8oMjCXztgoe95TVDYS2lsT+0JSoY+maJTUO5ee9anfzFi5Afunep7WHP6Wq32WAjZcRx+7dd+jZdeegmtNT/7sz/LqVOnHnnd+z7+d+1I3yW4rntXhd3jsuC8PYe8LyrRWnP8+HEKhcIdP7PWsvzDV1JOlQVhDK0WdM4pelYcRCxBCJQD5R2BGwmyQnDqmObzXzJU7jCVJgxDpqam2N3dpbu7m4mJie8Lhd1HCdtM2fkXNwheGqT9RhVdydO8tU16bgi91MI+M0GyHmKHPVItEEECqUFJSF2Ju9OgfXyAzNuLNM8Mk3lrgdbZUXLvLtA8NUz2+gqtk0MECxu0J/rx13eJhjrwV7fx623cjQWwHlGxTJDmSbs7cDc3iTs6yayvE1f6yKyvElf6yWysEpf7CbZWicu9ZJfmcCNwozrC70PJDNKTWOkiwjq62I2sLiIrY7B5g2uvOjgtw9TWMJgY0jZe0MfEGcPNy4pD4w1oJmzd7ECc1ixOKaRj6TmksSEMj2hUErD4rkOhx9I5LCHxiAWE7YT2uiFcDei9sIOyDitvZgg3Fb1nNPlew+rVDDsLHm7BMvxCim4LqrckOzclgy9qol2BtSAV9L+g+cQvxDj34fvzKOb0j0sY8rnPfe4jnwxyNzxxhHwvuK77WAhZKUUURVy9epVarcbExMQ9RSXWWv7Bt1ImCoJCBO2rEmdb7XlOGIFvwd8VeKkkay2nT1g+/2VNqeuDa72/YNfR0cHW1haNRmNvzNETVrC7H7RPfyfH134zJPtzQ9hejcn42M0Q4zsIKbCeQjUj0r4CzrVNkqM9ONc3SCd6cCe3SE714dzaIj4zgDu/RXyiD2ejRnKoE1VrYTuzyCjBbYSIrRV0zRCWuvFqlq2BcUpzS7SHRyjMzNEaHqN4a5b20Bj52Vu0hvd+hoOHyc3dIuwdoTh1A0WG/PocpmMcp7WMLfYhm9sYtwAiRiUxJltC1lfAGtTSZfzgJLY9jwpGMWkDYVNk0E3YmOTGNxQqUSxsFHBkBxMXDPOXFLmSZXDMsHVtr8CWLxsW33aojGi6hlI2LzvoUNF9LGX7Vo5ij6GzV4PJsnnFQYeCrme2iCPB8us5oq0cXWfbBHlJtKPYvbXXgdFzXpM0BUHZ4hUtn/xHMd1n7jy89k54lJTF97sXMjyBhPxRWHDejjRNWVpaYnNzk1OnTnHixIkPLRL+20sWuSap3RKEDUG2KVAJBG1wagJPOhQ0nD5p+PH/3lC4w74yxrC0tMT8/DzDw8MHBbsoimg2m0xPTxOGIa7rHkzsKBaL/NT5X3yk8/044HbC/fA/1iR/PIv3ExPoy9vIE12I6ztwtBNmdhATFcRSDTteQWy3sCNlRCOCniyEKTLvAqA8SeI5uK0qSaQRy21amRxprcry4BE6rs1SGz9Mx41ZakfGKE3NUjt8iPL0LeqHxyjenKU2dojizCyNQ2PkZ2dpd/dQunoN5eTJX5lD95/GXb6J7jmKszaD7jqM2ppH5wdRjS2Mm0fWV3Eb63jeMLK1hSydQdemUdkxTLSJFAFWGOz2NfLyKNps4MgiUmaJkhkm3xhEt2cJtz3acxNEdgW0Jrc8yNFPp9i24NZf+hR6Dd0nDK11SbnLIKxFJ7B2yaP3pCaTMaRRic1JhVCW8rkNhAiorwkaC5LSsRrRegYPg5eXHP6c5am/n9yXnefteJQuiyeBkJ84pR5w4BT1fszOzuJ5HgMDAw+8pjGGxcVF5ufnGRgYYHNz877URFeXLF/6P0E2IdsQBCHkWxLTBiex5IzhmfOKH/sHhuwdbA73C4VTU1N0dXUxNjZ2UMiDDxbs4jimVqtRq9X4H37kqw98nt9rPBD53g0ZRfbXP4NNDcbzsNWItJyF1SZmoISd2SUZ6YDJbZIjXcgbmyTj3cjrGyS9JfTkDokb0N41bI8Mklnaod7fS2Zlg0ZPF8HaDo2OCvmNGlGpRHanTpwv4NeaJJksme0aabGIv93AiVMKKzWEV8aLFLrYjbu1iq4M4G0skHaP4i/PoLuO4K7dRHcdwVu6gZMo3NhHOV0IBCKqIYI+qM2g8uOYxhwq0nixRCUKzxsliWZwZT9gScMl3BiUCVDGxRf9hHYOaXNYXUfqFFcXCGwfoVhDmzpnnhpj47Kk54ShuSmIdqFrbM/nItyFrauKwedSTGxpxw1olHCzFhMLhLK4xRSvu83of3MLyjtIKd9jsXk/E6/n5uYIguCBB0l8+tOf5s033/zI5vw9BvxHpd778TARsrWWtbU1ZmZm6O7u5oUXXkBKydra2od+dnHG8uV/DaWqIGhCpimxqcDRUErh6IkWL/zkEifPHLnj52u1Gjdu3DgoFN5Pwc7zvPsanfRxwWMh4A8sqkn+3SzefzGB2Y+Sr27D8S6Y3EaMdyBv7mDGK9jrmySpILy4Sb1YJl5zMT3DmFBDTqLilLgjhwoj0nwWmaTYjIvUhtSXYC3aEXuRirRgDV7YJl9LcLSHpBuRy4P0SDyDEzVJS504jW3izgHcnRWivkP4S1OoVJKdvI4qnYLmLCI7BNEuFgcyndBcRGT7YOMSGYaQxiIwqKCTKJzE9cZJ42Vka5e8mCARqziigFJFmmZvfSeN0Wg8enBliYadweo2xeQw0xfrxGKd+iu9xGodR2fpPtzHzoxAKRh6xpAkKWErIt0uUDls2JlSFIYNmQ7D/9/em8fXWZaJ+9e7nf2c7PvWJmlaWpauUBxgGARBBQesgzLyAwYZ5jNqwUER1K8LIgKCAsMiIA6bjgoOwoBMRZRd21KgQAtt06Zp9j0523ve827P74+QYwJNSdOkSdNz/UPTct7znO3Kfe7nfu67YY3NEZ8DSapFkiRc193r+KdgMDimg5umaZmXbjKbeiPB16HeehMOQyGn0+kJ//8DAwM0NjYSCoVYsWIFXq8382/7+maRjsNfb5H571ZBkQMeQ0JyJTwmhC1Yukpw9pUu8UScwcEP7jqPbNgZhkFDQwOhUGjObNhNi4D3gvX0HrQza1CqQzgpG7U0gJUwcQ0Hc/MARlohioJshtCLC/Aa/Rh5ufhae9FzQvi7e0hUlBDc0020opTgnm5i5WWEWzuJVpSR09rFYFkZua2dpCN55O9uQ1ZC+BKD2Lm1eOMdmLmlKINdOOEy1HgPTqAIxehFePy4moKcTqLqSYK9u1D8tSipLshvQAzsRMqpR8RawF+GZCUh3oZiSmjRLjy+o7GNViQ5H0lRsdJ7UOUCRGwbfrcYVVpM2mnCo1SBLEgZ7+I3c/CIAgypHb+oAQQJ9238Zj5+UUtK7sAhjex4ERjIroYjmTT91cSQWvE4Qdo7dVQnSO2yIhIDCnoX5DcIipa4rP6GiS/fQQgp8+0NIBgMEggEKCsry0h6pBdyb28vTU1NOI6D3+8nFAqRSCSIRCKTes2zQp6ljNcTeaKTp0ea/8iyzJIlSwiF9pJL2AuuDZt/LrPtcYlXQ+B6hmeheVLDIj56meDTV7n43rucnho7NWQunrA7WAL+AIaD+bvdSMeWkuq20PPzsAYsjAU1aI29GLUleHb1kqopJrC7B72qmMCeXvSqIvxtfaRqivG39aNXFxPo7Cf53n8TFSUEegdwfF5K3m1F0nKJ7DGxIvVogz0YRVX4+zpJ55fjHejAzCvH19eGHanEM9iOlVeOv2cPmunFG5XAPw8CaTCTuOEy5HgrIr8eBnYihWqQe7bjcfLQpDJcJ4oaLMdM7kT11uLaUYTRjWZLKOYAXrkOZBfD3o1frSdt7kIyDXLFkZhyH2m3l6BYgO7uAidFrr0IkEjIu5BcDcUFn52PoXShighCWLjuEIqkYcsGqh3GVQw6XnNIqV2YQwP0xP7C0J53Oe3WG4C/vT9HpOw4DkKIMRPEfT4fXq+X4uLizKCGdDpNPB6np6eHlpYWdu/enWlYPxJJjzejb6pa4c4G5sajmCAfVvY2EpmmUikaGhr2q65x+xMym38mYxuwJV+QVMGjQzgNS44WnPN1l/D7ugGOHFQZyU+3traO2bD7sBN2MDtlPGMSfh/WM630n3AUzJNxbMAPUsrEKQ0jGRZOYRDJtHHz/EiWjRvxIdkObsCDZDsQ0JBcF8mnoqRNvIkUnn4LyfFj+/ORPUFc1YcdtJCsNFYwgpzWSefkoaZimDnFKMkBjPwygj2taKZMcHc7sr8eKd2KyK0Eows8RbhuDNkxcMPFyEO7UCzQ2prwBo7GsbsAgaIVYad2owbrsWPv4E178YtqTLsFr7YA2+lDuBYKEUz9XfxOCR4KSNGMQhiFMLrzLpoTJujUYUlxUlInsuMSMisxlQEMpRvNycMVUTxODqYyiOz4cOUUPpGL7eoktXZinp10hP+IKw8PFR7vfTgymBb+JunRU8RH3uOappGfn09XVxf19fX4fD5s2yYejxOPx+nu7iaVSqGq6ph0RzAYJBqNTjqqnm3MSSGPJ6/xyt5Gmv/09/dTX18/4XacQgg6Nsj89SYFY0hC8Qn2hASJ1HCOeMni4dRE7l7qiGH4lF0ikWD9+vUUFRVx7LHH7nPDbjSzTcSzRcKjkdIOgT9sI/mZpXi295KuL8azo4d0fQnexh6M2lL8jd3o80sJ7OwhOa+U4K5uEvNKCTR1kc6LENzajqVFCMZi6KXzCcU6SBUWE+xuxyisINDTgVFYgb+vCzOnDHWwBytchCIlkdI6/mgCb49AlkuRLRMCITC6EcEqRLIVyVeFSLXj+stRunfi0RU8ahVSuhclXIWVaETx1eFaQ0hOGknI0LuViLwYlyi2O4BPqydt70ZxfaipFJLr4KMeZImkaMTrlmDbXUiuhN+tQCNCUm3DcWIEjRI0ESGptqC4XiQBmuvBlDXS6hCS7UWWFPz2PAyll5TWRVfoeRKePRN6Dfb2Ph0taRgWtG3bmfSFqqqZJkORSITc3NzMZ2GkYX08Hqe1tZXHH3+cxx57DCEEd9xxB8uWLWPFihUHPOz0yiuv5Mknn8Tj8VBXV8f9999/UHplzMkqi/F6IpumyZtvvsmqVauA4TfCnj17Ms1/KioqJpyH+vOjbxJ/cjmxVhnFJxAaNJqQUgT19YI1V7rkV45/+1gsxrvvvouu66xevRqPx3PIiXgmJTy4cGLjeoQi41x4Kvg8OCkLPBpO2gFNxTUchKoO/yyruEkbKWpg99sYShgbH47PhzeewvYH8MaTmKEw/sEYZigX/+AAZm4h/r4e0vklBHo6sUKFRNraUKUcPEkLyVeFnOpGaEXIVhzwDVdNWDpoOcjJDlQbvHEHn6jFcQdRTA1J8SL0DlR/DU6yCcWS8KQ1FEdG0yoxzWY8UjGS5ME0duJJa3hEAa4bxc88LDGA7cZRHAuPFcSWdILuPAQuCWkHmqWSYy4kLQ+QlvtRHC8KKqobxFB6kR0NV0oTMWux5ASG2suQbytdoecR0sTriifKlQ+dTUVFBZWVlZlc80gUPTrdMRpZlpEkifXr13PnnXdy5plnsnnzZr785S8fcLvMZ555hlNOOQVVVbnqqqsAuPHGGw/kkodvlcV4MhtJWeyr+c+HkeyBv1yvsPOlRYRzBWpEkDahA0FZneDsK1xK9l40AQz3RG5sbCSdTlNfX8/OnTvRNO2Q2bA7mBKeqHT3heS4yBu34350KUr3IE5ZEUrPUOa/dn4edAySwo+RhERuBQGtBytUgC/ai6uGkG0DoUSQXBsBuCogBLbPi2SZWMEgwa4OvLpMzkAK4a1HSfbhRCpRo224/kqURBvCX4mU6kFohciugdYfw2+XghVDlUuxnFY0uQrHO4iSFkj+MtyBLfhFOZKVRpNykFQ/aXMnXk89ltWOEh8kx1mESScg4VXmkXR3I9sOPjsHBx2QCbl1GHRiub3kpRuQhYeE2gwuSK4gaJeRUrsxlB5wZTxuCI9TTkrtJqm10hF+FkPrOeDXYzxuuuDxMZHzyH7J6M/l+yU98uc///nPGIbBpZdeOmXr+djHPpb58+rVq/ntb387ZdfeF3MyQnYcZ6+pCSEEL730EpqmkZeXR21t7YQHI1o6bLxNYdc6GVkBnShebwgRkvBWC/7+EpfyI8a//chXsr6+vszJPsdxeOutt0ilUvh8PnJycohEIkQikcy6DhcRT4V8x0NIEs4Fp0A4gBszEC4Y3Sl04Ue3vKSDEdRoHCOYgy82RDqcT3CwHzNUiG+oFzNSTGCwBzNUQrizg2RJOaGODoQaINwdQ9Yq0FJxXH8JijGEUELIroXkuKD6UJNR8BaixNuQXQVvLI1X1CLcIWThQ0JF2IOocgm23YpGCSLdRmDAi6aWYxu78HoacOxBcG0UKYST2EnAqUYliOHuxi/qAAvDbsJnBvGKElJSCwFRg4RGwt2KzwoTdOZhSXEMuQvZBr9ThCQUUmo3kqOA5JBj1pOWh0hpXfT7X6c3sH6C8d3kuW/DVYTD4f3anOvp6eGrX/0qsizz/e9/nyOO2McH8AA466yz+OxnP8v5559/IJeZ0DN42Ah5pPlPLBbj+OOPJxAITOhargNvPyjz1i8UEMNTDywbEk6M8mM1ln9Wo3If345Gb9hVV1dnDqWMTk/A8IbiyIGOWCyGaZrcfOETk3j0U8d0SXg65Tsedn05xsJ69IRErKAC70AfergY71A/eqQAb2yQpD8PTzKG6YvgSesgB1CsNELyIAsXxRKotkVgIE4gmYPHEDjBQrRoJ3aoDG2oDTdchRprxw1WIOt9CE8eSjqKdzBBwCxAsg1ktQTXbEFVqnGdPmQRRkJCWP2oloOWdPFb1QgphWvG0LQyLGMXmlKBq7fgSckE5AVYbj8uabxyOYa1GzmdIsc5grTUgxA2fipJiT24TowccyEyHpJKC64wUW2FkF2DrnbiSClwXYJ2OYrrJaV2E/fsoj3yRywlNq2vy/2bvkk8HicWi5FIJHAch0AgkDlpOjLncTRCCP7nf/6Hm266iWuuuYZzzjlnUiVvp556Kl1dXR/4++uuu45//Md/zPx506ZNPPbYYwdaVnf4Ctl13Ux5m67r7NixA9u2aWhoYMuWLXzkIx+Z0HV2/p/Mq7fJ2CkJT67AdkGLwPzTXJQF25l3RMG4gxSFEJmWmEVFRcybN++Q2bCbahHPhIDfjwA6PnoGZl4+yuAgZk4eWt8gRk4BnoE+UrmFePt6SOax9n74AAAgAElEQVSWEOzvRs8rJdTfRTpSRrC/A8VWCUZdJKUKxRpEFvlIbhJJ+JAdF8m2EGoALTmIGyhCjbYjST4C/VG8bi2SE0UijCQEwk0iq/m4ZiuqUoVrtqEaLoFUIUIk8TolmHIHHqsYcHGMdmTHwaOreN08VCmXlLsLr1QJQmCmG4mYdSj40KXd+EQ5CAnD2YXXzifglmNLCXS5A8lxiFi1uJjDUbGQkR2ZsD2PtDKArnbQE1jPYOCtaX9N3r+5B8Ofm2QymamuiMfjmKaJ3+/npZdewuv18n//938UFhZy2223UVi4l4YvU8QDDzzAPffcw5/+9KcJB3D74PDNIcPwBt7OnTuJRqM0NDRkmv/Isjyh8/KpfrB1aDh7uAF3uAYK6l3yakGSoLGRcUvoRqJxn8/HsmXLMht2szlPPBclPBoJyH97M10nnYIsv/f8exUQLq7Ph+Q42OEwsm2SiuShGEkQMoXNnShSBWo6jvAUoKS6cL2lyHoHqBWQ7kRo5SjpOLYWxNE0vH2t+FN+tLSMrC1AmK3IWjXC6gSpBEn2IpwYkpKDFN1JbqoWRxpAFhoSBaSVDrxOOabajWQbhPUcHHsAn1KDK6dI2XvwMR/T3IZq+cjlaEylH1P0EXTr0d1tSI4gYi1AwYuutGC7KfzpXHxuEbrajoOBEA5hsxYQJLQWop7tdET+iCMb0/pa7E3EmddJkgiFQoRCoQ/MeXziiSd49tlnkSSJrq4uvvCFL/D4449Py4GQdevW8aMf/YgXXnhhKmQ8YeZkhKzrOuvXr6e2tpbS0tIxL9hrr73GkUceOebU3WTYvXs3Xq93TF+MkQ070zRZsGAB4XA4swEx10U82wQ8Hl0n/AOp0jI8vb2kCorw9vSg55Xi6+0iWVBKuK0d2fLiT8jgrUAx+nG1fGQ7DgSRhQ2uC7IX1YghKfnI6W6QQ/iivYRilchmDJQiJDeF5AgkOYCU7kHWynDNVhQRQk3G8acKUAhi047XqcKS+lBEEAkPtr2bYLIQxZHBdfDa+aSdPahyEcIcACNOUNQi43kvKi7FcRIIawiPE8Hvlr0XFbciO5BjLsSS43/btHOCBJxSDKWXpNZGV+gl4t6d0/7870vG49HV1cV//Md/EIlEuPXWWzPB1cDAwLjfUA+U+vp60ul05r5Wr17N3XfffSCXPHxTFkIIDMPY68m2N998k7q6ugmfvhuPlpYWAKqrqz8wxLSwsDBzQmk2ivhwk/Bo0jm5dJx6BoqewvT4kG0LEia+aBo1GQC1AMWI43pz0fQeXG8xqt6J6ytD1TtwvRXIRg/CU4xkRdH0NP4k+PThgxeu6EFzSyHViuypQlj9SESQEEipbnwpDTXt4KEahyFkR0MmgEUbPqcKU+zGl/QSSlWge1rwm5UIycY221DdXDD6UR0/AVGFxRAWUbyiEMtsQ3Ekgs6893LFe3DcJGGzGkX40dU2XGEhcMg1F+BIKXStmyHvVjrDzyGkA29Luy8mI2LXdXnkkUe45ZZbuO666zjrrLMO5ePRh3fKYrxjxlPZpN4wDPbs2UNbWxs1NTWZJvEj159tMp4KEU+3hON1U1/jOkJ4l4w3OkRoTzN6WQWhPZ245KEmXOxgNZLbjZBkkFyEcHG0ILgmtq8Q2Upg+0uHI2ZPLv6BZvypIhTLRBXluMogwnGQpTyEPYTkr8JNtSF7KpHiu/ClwnjNInAtVHIxaRmWsjIEjo4sPLjGLvL1emw5gaH1ETCrMbQuZMePZLtI6QF8VKPIPhLsxG+XIbsWjt2F18nF75RgSXHi0i40y0e+vZi03E9K7QQXAnYRmhseVcr2J1Ja57Q93yNMRsadnZ185StfIT8/nxdeeGHaIuHZxpyMkIFxmwjt2LGDvLy8MVOa9xchBI2NjbS1tVFdXU1NTc2s3rA7UBFPh4SnU7wfhiv7iYbXIAkZyXYQqg8tFcP15uKN9+L4itGSndj+crRkB66vHMXoRcJDYChBIFmEJDxIro5MLo7oQBXlOHTgccpxiaJYPpRUP76oTcCej0krHqpwRRzJZfh4My0oIoCq6/j1XDxODrqnFb9ZjsAlrXQN95eIB5DSKfxUYTGITRzFUVFMC1dYBN15SMgkpSawDXLTixC46FobuBKScIlYdaTlIQy1mwH/W3QHXwZpej/Ok42Kf/WrX3H77bfzwx/+kE9+8pOHclQ8msM7Qh6vwdCBRsjRaJTt27ejKApFRUXMnz9/1m7YHYiIp1LCMynfvSG7KXzpLRj+lchuF0IKAMO5ftvrB9fG9hUgWUksfwmBgVb8qSAeI40sz8OVOlEpw5UFuBayVIQrhlAox5LbUCyZQE8Mr10NmNgM4KEKixY0qRpHjuLaXXgNFcVMEbBqcCSdtNpLwKzC0LoQjkkoFsGW43jTEWTy0dmJR+SjmhaSY6OKHLyiAFMaxBAdBFNF+N16UkoXlhQH1yVkVSGhkNBa0LV22sLrMNXBaX+OJyPjjo4OLr/8ckpKSnjhhRfmRMP5/WXOCnk8JivkVCrFjh07sCyLRYsWIYRg69atdHZ2kpOTM24nqoMt4tkQDc82Ae8Nn/EWpqcBRytFsfqwAoV4Y13YwVK8sU5cLY/AYB9+owTFLkR2/UgSCDGELJfhOJ0oUhmu1IEqKnAlF5FuI3cwF0QaL8XYciseUYUr2zhuHI1qTKcJr+nFq4dRXBnNiZDSWvFZFUhoJLXd+PUAnnQermQQ1qsx6ccSxnt10CY2UuYYdEx+F9WUKDSXYEtJYtpOcFU010/AKsdQezGUPvr8m+gPvjbtz+tko+Jf/vKX3Hnnndxwww18/OMfnytR8X4zZ4W8rxacqVRqwtcZvWE3+oSd67rU1dURjUbp6urCMAx8Pl/mpF1OTg7nHfmdqXxI+2Qmo+FDQcDvR8LFn1pPMvQxhKwghIsZysUX7cWfUAjELWSlDmF3IsnluKIDlfL3juzaIBfgOjEkqRBJbyJvqAJXctDSYYTsxVSH8NhVmE4LHqkaW+pC1vvJT8wnrbXjcXOxpSRppR+/VYWu7kEzoaB/HnqgDdUuRCJELNSCNyrhTWs4koTiBvFRSkrqwHYHyE3UoeAloe5BCBdch4g5D1vWiXt2o6tttEXWYSvJaX9Or/7lGrZv35451BEMBj9UrO3t7Vx22WVUVFTw4osvHpQGPrOZOZtDtixrrw1Jent7GRwcpKGhYZ+3d12X1tbWzIZdeXn5mCYn709PjPR0jUajfPHEW6b2weyDyYr4cJTw3oiHTsdWywjE2gkkCtDMNJpZDs4QEEbCQbJNJDkMdheKVIrrtiNJ+WiJHiKDJSiuF0eO4rEKMTxtBFKV2Eoc2ZYBCTnRTk6sFldOIgkVVYRIaS34rWpsKYFrd5E7WIOj6AgcfFYBhrcP4dp4hnQ0N4iLScCtwiFFUmrClw4TsqtJy/2klQEkR8XrhjObdqYyRHfwZaK+bdP+HI5ExZZlZU7dxWIxdF1HUZRMT+MRSY/stzz88MP89Kc/5Uc/+hGnn376XI+KD9+yNxhfyENDQ3R0dIzbDUoIQU9PD7t27aK4uHjWbtjNhIjnioRH4xLGGz8H2fEiiTSKG8aVu1CtUrDbkeUKhNOHJAqANLKdxJMy8cdk/OkK0lonXqsMR9aRXBfVCZPW2vCmi5CTbQQTJahumLTcRsCqwpajCCGhihCGtIucgRK8VphEoJWQXo2QbHRvJ4oNoUQhptNO0K5BxkNC3gl2mjzjCFzJIqm2ojh+hJQibM4npfZiyTESnj20h/+Q6VU8nXxYimKkp3EsFiMej7Np0ybuuOMOhBAUFRVx7bXXsnr16gM+F3AIkN3U2xv7mqs3NDTEjh07CAQCLF++PNOFbTZt2B1sEU+nhEPzo5O+bWJ3zpSsQSaOq21FcY7DVQZR3DCIMEKkkZQyXKcfWSmE9B58ug9fQsVjVoBkYylDeK0yDE8bPrMSSxlEEjqyDd7+HoLmAky5D5c0PrcK3dMyXMomt6KkhihKNmB4erFcnbBeQ9LXgWS7hOIRbMXAtZMEWYCpDmLaO4joVXjcHJJqGy4WkivjcyK4BIh7dmPLOu3hZ0h6WqbkudkXE80Vq6pKXl4eeXl5uK7Lq6++itfr5cILL0RRFB588EHa2tr4/Oc/P80rPjSYs0Iej701qR/pd+E4DosWLSIUCs0JEc8GCR+IdPfnugciaMf7BopZj+wWY2ntaFYFtrcDzSxHctP4hroIxWpwlCE0pxDT24YvXYktp3DdNF6zgrTWgWILtESKUKwMCQlD7cBnl2PKfeCC6kaw7EYKow3DEa6vjaBRia3oxLVWfGkZXyqflG+ASKISF5sY7+AxPeRbR2IqQ0S1RjzWcCrFZxeTUrtxJZOobzsdoT/BNPQqHs1kNu1g+CDV2rVrqaur48UXXyQcDk/xyuYGc1bIE4mQLcti165dDA4OjtmwcxxnnzPs4ODI+GBGw1Mh4emS7/7c96TELLlYgefwJD6N5BbgSElkV8Pft4dwsg5T6UBGRQgfDjoeu5K0pxOvWYbp6UKxHCJ9IWTHxp8qQg924k8Wo4kiDLVjeCSS005oqBiv00DS147fKCJoVBL3N+NJS+QPlJEMdCO5MpFEJbq0B9dJkG80AIK4uhPViSC54LUjpJUBklobtqzTmvO/GGrv1D6he2GyFRT3338/9913Hz/+8Y/56Ec/Oq254osvvpinnnqK4uJitmzZAgwfsf7sZz9Lc3Mz8+bN45FHHpm1JXVzNoe8r57If/nLX6ioqKC9vX1CG3ajma0ingkJz6SAP4zJiFnVP4JqlhEYsokMVCNIIwkbxQ1jKe14zQospQfVKURg47qd5Azk4cgJQolKHCWNIyfxGfmklXY0pxjH7cSblAilqrGUBC4GfrMIw9OP68QJJ/JwZRuBIGAUYqlJDLuZoFGEzy0mqbQiJAfF8aE4AkmomMoQslDpCa6nN/DXae9VPNmoeM+ePXz5y19m0aJF3HjjjQfcrmAivPjii4RCIS644IKMkL/+9a+Tn5/P1VdfzQ033MDg4OCBTv+YDIf3pt7oFpwjCCHo7u7mrbfeoq6ujpqamsy4GDg8RHwgEp7NAt4b+ytlyVUo33YeHiOfVKgNf6ISW+5HtfKQcHFJoDl5mNIuwkP5eAwvkgMeO0Qi1EYoUYmt6khWGuGm8CRMQnolEiq6v5VgqhpXskh52vHpXkLxQpLBLsLxKkAQDTfjHbDIsRaSlgffK4krwZS68FlFpNV+JCGTVgbYk/sYlhKfniduFJONin/+859z//33c8stt3DyyScf1AqK5uZmzjzzzIyQFy5cyPPPP09ZWRmdnZ2cfPLJbN++/aCt5z0O70299zM0NMT27dsJhUIEAgHmzZs3azqxzVYRH2oCPlCE7NA7bx1l28/FlywblrFbgKW147UqEVISJW5SGltAMtiGZhdgeoawRYpQopJkqBVvwo+WTONJ+fHZFRieXlQ7SDBVTdLXgmwLCruq0INduJJNJF5N0t+NLSXJ6y9HtiXi6k48TiGq7RnucyFrpNU+FNdPW+RpBv1vT/tzMdmoePfu3axdu5YlS5bwyiuvEAwGp3hl+093d3emlWdpaSnd3d0zvKLxmfNCHr1ht3jxYoLBIJs2bWLr1q3k5OSQk5MzbgH7dMt4f0WclfD+EZof3e8o2Qz0MVjxCgVtf4+Ehksa2fUhJZsp7a/F8PXiYhNIlqP7OwmkyjC8fThWGi2l4I0OV0w4UpqUtxN/ugxTjZJQdxMZKgLhYPgHCCcqsVSdaKgJfzJEbnI+SbUFWVHx2aWYdKEKL6YSw+PkEPPtoCXyv9PeqxgmJ2PHcbjvvvt46KGHuPXWWznppJNmZV3xvoKv2cCcFbLjOGzbti1zCCQ/Pz+zYbd06VISiQTRaJQ9e/aQSCRQFCVzwi4nJwefz5d5Y061mKdTxIe7hKeCWPGbhLtqUJxc1GQXef3zEFIehrcfn1GEHujAr5fhMwrR/V0oto03qRGMFaAIH/FAC0G9Cm+6mISvCZ8epCBZRTLQSTgxnJ4YjDSjmlDQW0PaNyzsoF2DLjfjugJkAa6CRoimvP8m7m2a9sf9nUfPQ9d1XnvttcxBjkgkMm5bgBGamppYu3YtxxxzDC+//PKsiIpHU1JSQmdnZyZlUVxcPNNLGpc5K2RJksjJyaGhoeEDLTFlWc6IdwTLsjInjLq6ujKDRyORCPf85Wv4/X5aWlpIJpNc/8+Tm0A7m0Q8lRL+WPXU5eOeaVk4Zdc6EOK+PzJv5+fwmrUkg20Ek5XIwo+pxgno5SSDrSi2TG5PCCFbBONFpNUBXNchaFaTDLagpgUFPfPQA50IbCKJ4fSEIwxyBwqQXZVYpJ1QtBCZHAyakV2BkFxCZjWd4edoDz8z7b2KYWxUbJpm5rPQ3d2Nrut4PJ4xc+78fj9CCO69915++ctfZqLi2cinPvUpHnzwQa6++moefPDBzLy82cic3dSLxWJEo1Fyc3MzX1P256vKyFHowcFB2traiMfjaJqWEXlOTg7hcDgzCmpfUfRsEfFUSHgq5fthTIWcJ1NtEd41XO7oMQqo2fVPKK4XPdBOQK/A9AwiXINg1IerJMntr8KRLUy1D79ZhqVEsRggZ6gEIZkIXPzpAkwtQVodwJtWCcVKiEc68KYieNIhkkojiqsiCYWAVYauddGU+9+kPB8cwDnVTDQ9MVrSO3bs4Gtf+xqWZVFSUsJll13GySefTHV19TSv9sM577zzeP755+nr66OkpIRrrrmGs88+m3PPPZeWlhZqamp45JFHZqK/8uFdZbFx40a++tWvEo1GWbRoEStWrGDVqlUcc8wx+P3+D739SEVGc3MzpaWlVFdXI0kSyWQyI/t4PI4QgnA4vNd89JqGq/dLxhMV8cGS8MGU73gcqJQPRMgAwdg8KvechZAEKW8HgYQHb0rDYwRRHR+x3DYi/RVIuOiePQQSYQLJXJL+biLJKlzJJhFsQzElcgfLSAUGQUAoWYIutSNEEkko+O0SZFRaIk8elF7FMPlc8U9/+lN+/etfc80116BpGq+99hrl5eX8y7/8yzSscs5weAt5BMuy2Lp1K+vXr+fVV19l8+bNyLLMsmXLWL58OatWraKhoWHM0NORIaWhUIi6uroPjCEfjeM4mbP60WiUZDKJqqqZfHQkEsHn82Uk/YlP3z7m9rMpGp4NAt4bByLl/RXyaBmPkNe7lPyeenJ7CjF9cYKJIlKBAVTTh2YH0D3NqCmZ/P4qkqE2AskyFKERD7YjWxJ+3YcsZNKeBJFYOY5sobMTxfHgs4vxihwGvG+zO/cRLHX68/mTraDYsWMHl112GcceeyzXXnvthAKbqeKWW27hvvvuQ5IkjjrqKO6//358Pt9Bu/8pICvkvSGEIJFI8Nprr2UkvWPHDgoLC2loaOCdd97hrLPO4sILL5z08U7LsohGoxlJj7TmHImiI5EImqYBcPw37tnntQ5XCb+fyUp5KoQMULHrOKqajsdRTFL+IUKJYkx1AMeNkddfgq0kURwvXiuC4R3EIY3sWO/VGvcQjpehuB4Gc3ajxQx8VjE+twBTjtGU+xuGDkIpG0xOxrZtc9ddd/Hoo49y++2385GPfGQaVjY+7e3tnHDCCbzzzjv4/X7OPfdcPvGJT3DRRRcd1HUcINk65L0hSRLhcJiTTz6Zk08+GRiOcq+44gqefvppVq9ezR/+8Acefvhh6uvrWbFiBStXrmTZsmWEQqEJ5aE1TaOwsJDCwkLgb0NXY7EY/f397N69G9u2CQaD3HXusei6Tl1dHSUlJUiSlJH0RGQ8lyV8oEyVjAHa6zaAJKja9RH8eh5JrZlgPITXKMHUYoT0UmzFIB5sR7FdwrE8Uv4BXMkhN1qD7u8n7RkkOBAm4MwHoCP4ZzrCz2Ar+gE9zokw2ah427ZtXHbZZfzd3/0dr7zyyoxFpbZtk0ql0DQNXdfHTHufSxx2EfJ4rFu3jlNPPRVVHf4d5TgO27dvZ8OGDWzYsIE33ngDy7I4+uijM5JevHhxJtLdH0ZafO7cuZNQKISqqiQSicwvi5EoenQ++sj7fjrmGvsj4rkg4MlEyPsj5H3JeDRlu1dQ3jifyGA5yWAb4cTwRlYi2IpXD6FYFkguiu0hkCrAkSyiOc34jBDhWAkSMnFPE62R3xPzNu73Y5oMk42K77jjDh577DHuvPNOjjvuuGlY2cS57bbb+Na3voXf7+djH/sYv/zlL2d0PZMgm7KYanRd54033mDjxo1s3LiRd955h3A4nBH0qlWrqKys3GdTokQiwfbt2/H5fNTX14/pAzuSj45Go0SjUXRdR1XVjKBH6qNHWP2n8T9o0yHh/y/vLxP6/x4enPqvtLNFyADz189nXsvHUVwvyUAHWjqMyyDelB9XtgknyhAIhnKbkB2J/P7hIaSmPERX8CW6Qs/jyntvATuVTDYqfvfdd1m7di1///d/z3e/+90Zz9UODg6yZs0afvOb35Cbm8s//dM/8ZnPfIbzzz9/Rte1n2SFPN0IIejv72fjxo1s2LCBjRs30traSnV1NatWrWLFihWsWLGC3Nxcuru76ejowHEcGhoaxtRA74uRcqORnLRhGPj9/oykR+ejRwR9IDKeqHQnylTJeX+FPF0yzts+3PTda+RTt/tsJNvGk5KxVZOcaMVwBBzqwFJ1CvqqUVwPlpxgyLuNrtBzJD2t+/U4Jstko+LbbruN//3f/+Wuu+5i1apV07Cy/efRRx9l3bp1/PznPwfgoYceYv369dx1110zvLL9IivkmcB1XZqamjKpjo0bN9LW1oYkSVxwwQWcdtppHHPMMZOekDCSjx6JomOxGI7jEAqFMpIOh8PIskxfXx//OXjlPq831QIejwMV83QJeTIyHkFyFKpaVlPZeiyK4yHlG8TwDBLQcwjqBdiSTlJrY8i3hc7Qi9PeqxjgyofOzoxNGvmFPZHZdu+88w5r167llFNO4Tvf+c6smuCxYcMGLr74Yl599VX8fj8XXXQRK1euZO3atTO9tP0hK+SZxnVdTjnlFE488UROO+003n77bTZs2MDbb7+Nx+Nh2bJlrFy5kpUrV1JfX7/PVMeH3U8ymRwjacMw0DSNqqoqCgsLCQQCmQ/ldxr/5aCJeDQHIuX9EfLBkPFotHSQmt1/RyCRR35/zXAlhtyOofbTFvk/0mrfhO9nsoyOiG3bzhziGD3bbkTQkUgk836wLItbb72V3//+99x1112sXLly2tc6Gb773e/ym9/8BlVVWbZsGffdd9+s+qUxAbJCng3ouk4gEBjzd0IIYrEYr776aiaK3rVrF2VlZZl89MqVKykqKtqv04WO49Dc3ExfXx+1tbWoqpoRdDKZxOPxjMlHj35DN/YdnCPLk5XyRIV8sGU8GtlRKeitpWRHJTFvI73B9RO+jwNhIumJ0a0BYrEYv/vd73jmmWdIJBIsXbqUH/zgByxcuHBWN945xMkK+VBCCEFbWxvr16/PbBoODAzQ0NCQEfTSpUvHRLqjb9vT00NTUxMVFRXjbiym0+kx+eh0Ok0gEBhziGWkymS6BD0ZIU91dDxRGU9UxKPxb2nf79tMlslu2lmWxU9+8hOeffZZzj33XGKxGJs2beLf//3fOeOMM6Z4lVneIyvkQx3btnn33XczB1jeeOMNhBAcc8wxGUmnUik2b97M8ccfz4IFC/Z5qvD9CCFIpVIZQY/ko0fyjzk5OYRCoYzcp0LS0ynkmZTxwRQxTF7Gb7/9Npdddhkf//jH+eY3v7lf75cDZWhoiEsuuYQtW7YgSRL/9V//xfHHH3/Q7n+GyQp5riGEIJlM8tprr/Hiiy/y8MMPE4/HOfLIIznqqKMypXfl5eWT/urpum6mNenI6PbR+cecnBx0XWfnzp2UlpZihU7fr+vvr5CzMh7LZEVsmiY333wzzz77LHfffTdLly6d4pV9OBdeeCEnnngil1xyCaZpous6ubm5B30dM0RWyHOZ//f//h/z58/noosuoq+vL1PV8eqrr9LZ2cn8+fMzDZWWLVtGJBKZtKRHNon6+/vp7OzMRNG5ubmZ4+CjI619RdLTIeSsjPfNm2++yeWXX86ZZ57J1VdffVCj4hGi0ShLly6lqanpcM1TZ4V8uOK6Lo2NjZl89Ouvv45hGBx55JEZSS9ZsmTCH0zXdWlpaaGrq4v6+noKCwszR8FHctKmaRIMBjNRdDgc3ms+en+EnJXxMJMVcTqd5qabbuK5557jnnvu4eijj57ilU2czZs3c+mll7J48WLefPNNVqxYwW233TbrmtlPI1khZ/kb6XSazZs3Z/LRW7ZsIRAIsHz58kw+et68eR/YDBwYGKCxsZGioqK9/vsIQgh0XR+TjxZCZOqjR1qTjtz+O437btU4m2V8KETFmzdv5vLLL+fss8/m61//+qSO+E8lmzZtYvXq1bzyyiscd9xxXH755UQiEa699toZXddBJCvkLOMjhGBwcJBXX301I+nm5mYqKytZuXIldXV1PP7443zpS19ixYoVk2q16LrumNak443KGl0fPcJUCPlQlvGBRMU33ngjL730EnfffTdHHXXUFK9scnR1dbF69Wqam5sBeOmll7jhhhv4/e9/P7MLO3hkhTwe3/72t3niiSeQZZni4mIeeOCBOds9an9wXZddu3Zx3XXX8fTTT7NkyRIGBgbGNPg/+uijD6gP7uh62Gg0OmZUViAQoLe3F9d1WbhwIX6/f9x+HXNZxj/5479nNlFH9+n+MF5//XW+8pWvsGbNGr72ta/NeFT8fk488UTuu+8+Fi5cyPe+9z2SySQ33XTTTC/rYJEV8njEYjEikQgA//mf/8k777zD3XffPcOrmh0MDAxw55138tWvfpVAIIBlWWzZsiWTj37rrbdQFGVMg/8FCxbslzhGM3IUfPfu3fhd3+EAAAsISURBVPT09GQOqwSDwb2Oynp/17u9MREZz8Z88W+3X585cTlS4eK67phj0CPH4kdjGAbXX389f/3rX7nnnntYsmTJtK91MmzevDlTYVFbW8v9999PXl7eTC/rYJEV8kS4/vrraWlp4ac//fAPepZhgcbj8TEN/kdyzKO73o30dv4w4vE427ZtIycnJ3O6cKS8b7xRWZFIZExv6tGSnmoZz3SKYnTaZ0TSsizjOA6vvfYaRUVF3H777Xzuc5/jiiuuyGykZpl1ZIW8L771rW/x0EMPkZOTw3PPPUdRUdFML+mQRQhBR0cHGzduzEi6t7eXBQsWZDreLV++fEyTG8dxaGpqYmhoiEWLFn3odJb9HZU13iSW2SbjyXZla2xs5Pvf/z5vv/02Xq+X0tJSPv/5z3PJJZdMwyqzTAGHt5BPPfVUuro+OLX3uuuuGzMG/Prrr8cwDK655poDvs8rr7ySJ598Eo/HQ11dHffff//hVPg+Bsdx2LZtW6ZXx+uvv47jOBx99NGEQiFef/11fvazn1FTUzPputSRfPRIU6V9jcqCD84z3BezVcbwtwG+5513Hl/5yldQVZX+/n4GBgZYsGDBFK8yyxRxeAt5orS0tPCJT3yCLVu2HPC1nnnmGU455RRUVeWqq64C4MYbbzzg684Vdu3axRe+8AVisRj19fVs376dSCQyJtVRUVEx6a53o0dljeRhR0Zl+Xw++vv7ycvLo76+HkVR9iro2SziVCrFD37wA15//XXuueceFi1aNMUrmxiO47By5UoqKip46qmnZmQNhyBZIY9HY2NjJpK4/fbbeeGFF/jtb387pffxu9/9jt/+9reH4qiZaaO1tZV33nmH008fPm4thKCvr29Mg/+2tjZqamoytdErVqwgJyfngE4ZNjY20t/fTzgcxjCMfY7KWtNw9ZQ93r0xWRmvX7+er33ta5x//vlcfvnlk95EnQp+8pOfsGnTJmKxWFbIEycr5PFYs2YN27dvR5ZlampquPvuu6moqJjS+zjrrLP47Gc/e6iNmZlxRkrvRgS9adMmdF1n8eLFGUkfddRRE+qFOzQ0xPbt2ykpKaG6ujoTeU9kVJbX651SSU9WxLquc+2117J582Z+9rOf0dDQcMBrORDa2tq48MIL+da3vsVPfvKTrJAnTlbI08FEctPXXXcdmzZt4rHHHjtcz+1PKaZp8uabb2b6dWzZsgWv1zumwX9dXV1GuOl0mqamJlKpFIsWLfpAP+rx7mOio7Jg4pKerIgB/vKXv3DllVdy4YUXsnbt2hmNikf4zGc+wze+8Q3i8Tg333xzVsgTJyvkmeCBBx7gnnvu4U9/+tOERDARHn30Ub73ve/x7rvvsnHjxlk71eFgIYQgGo2OafDf1NREeXk5+fn5vPXWWzzwwAMsXrz4gPPRExmVBXsX9GRlnEwm+f73v8+WLVu49957Z81G3VNPPcXTTz/NXXfdxfPPP58V8v6RFfLBZt26dVxxxRW88MILU1pG9+677yLLMv/2b//GzTfffNgLeW/09/dz/vnnk0gkWL58OZs3b2ZwcPADDf79fv8BtSYdPSorkUggSRLBYDBThrd48eJJT2kWQvDKK69w1VVXcfHFF/PFL35xVkTFI3zjG9/g4YcfRlXVzObppz/9aX7xi1/M9NIOBbJCPtjU19eTTqcpKCgAYPXq1VN6AvDkk0/OCnkcDMPg5Zdf5tRTT838nW3bbN26NdOW9I033kCSpDEN/hcuXHhApww7OztpamoiNzc3I+x9jcoaj2Qyyfe+9z22bdvGvffeS11d3aTWdLDIRsj7zYSEnD3WM4Xs3Llzppdw2OLz+cbIGEBVVY455hiOOeYYLr300swJwE2bNrFx40ZuvPFGtm/fTn5+/pjSu7Kysg+NotPpNNu2bUNRFI477rgx+eXRo7La2tr2OSpLCMFLL73E1Vdfzb/+679y++23TzrNkuXQJxshzxImslmYjZCnHiEE3d3dYxr8d3V1UVtbO6bBfzgcRpIkXNelvb2dtrY2FixYQGFh4YTu4/2jsjZs2MALL7yAZVkMDQ3xi1/8YsYrKLJMK9mUxVxjKoW8bt06Lr/8chzH4ZJLLuHqq6e3/vZQwnVdduzYMabBv2mazJ8/n127drFmzRq++MUvTrrrnRCCZ599lhtuuIHa2lo0TWPLli1cdNFFfPnLX57iR5NllpAV8lxjqoTsOA4NDQ388Y9/pLKyklWrVvGrX/2KxYsXT9FK5x533303t9xyC6effjr9/f1s3bqVYDA4psF/TU3Nh6Yb4vE43/72t2lububee+9l3rx5mX8TQkxrmWRraysXXHAB3d3dSJLEpZdeyuWXXz5t95dlDNkc8lzhd7/7HWvXrqW3t5dPfvKTLF26lD/84Q+Tvt7GjRupr6+ntrYWgM997nM88cQTWSHvg8WLF/PGG29kShmFEAwMDGQa/D/yyCPs2bOHqqqqMacM8/LykCQJIQTPP/883/zmN/nSl77E3Xff/QF5T3fNuqqq/PjHP2b58uXE43FWrFjBaaedln3dZxFZIR8CnHPOOZxzzjlTdr329naqqqoyP1dWVrJhw4Ypu/5c5KSTThrzsyRJFBQUcMYZZ3DGGWcAw6mO5uZm1q9fz3PPPcdNN91EPB6noaGBnp4e/H4/Tz75JNXV1TPxECgrK6OsrAyAcDjMEUccQXt7e1bIs4iskLNkmSJkWaa2tpba2lr++Z//GRjuSPfWW2/x5JNP8p3vfGfWVFA0NzfzxhtvcNxxx830UrKMIivkw5CKigpaW1szP7e1tU1ZL4+LL76Yp556iuLi4inpoHeoo2lapif0bCGRSLBmzRpuvfXWzOScLLOD2fHrOstBZdWqVTQ2NrJ7925M0+TXv/41n/rUp6bk2hdddBHr1q2bkmtlmXosy2LNmjV8/vOf59Of/vRMLyfL+8hGyIchqqpyxx13cPrpp+M4DhdffPGUzWE76aSTMpOFs8wuhBB84Qtf4IgjjuCKK66Y6eVk2QvZsrcsU05zczNnnnlmNmUxy3j55Zc58cQTOeqoozK57B/+8Id84hOfmOGVHRZky96yZMnyN0444QT2MwDLcpDJ5pCzHDK0trbyD//wDyxevJglS5Zw2223zfSSsmSZUrIRcpZDhuzBhixznWyEnGVKOe+88zj++OPZvn07lZWV/PznP5+ya5eVlbF8+XJg7MGGw4l169axcOFC6uvrueGGyU8jyTI7yW7qZTkkaW5u5qSTTmLLli2HTS1ttgfJIc2ENvWyEXKWQ47D9WDD6B4kHo8n04Mky9whK+QshxTTdbDBMAyOPfZYjjnmGJYsWcJ3v/vdKbv2VLG3HiSHW8pmrpPd1MtyyDCdBxu8Xi9//vOfCYVCWJbFCSecwMc//nFWr149pfeTJcu+2N8ccpYsM4YkSScALwFvA+57f/1NIcTTU3w/AeBl4N+FELOmDZ4kSccD3xNCnP7ez98AEEJcP6MLyzJlZIWcJct7SJKkAK8B9cCdQoirZnhJY5AkSQV2AB8F2oFXgX8WQmyd0YVlmTKyOeQsWd5DCOEIIZYClcCxkiQdOdNrGo0Qwga+DPwBeBd4JCvjuUU2Qs6SZS9IkvQdQBdC3DzTa8ly+JCNkLNkASRJKpIkKfe9P/uB04BtM7uqLIcb2SqLLFmGKQMefC+PLDOcDnhqhteU5TAjm7LIkiVLlllCNmWRJUuWLLOErJCzZMmSZZaQFXKWLFmyzBKyQs6SJUuWWcL/D+Bq5z73GY+mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b8efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "X = np.linspace(-np.pi, np.pi)\n",
    "Y = np.linspace(0,10)\n",
    "X, Y = np.meshgrid(X,Y)\n",
    "\n",
    "R = Y * np.cos(X/2)**2\n",
    "Z = (10-Y) * np.cos(X/2)**2\n",
    "\n",
    "ax.plot_surface(X, Y, Z, rstride=1, cstride=1,cmap=plt.get_cmap('rainbow'))\n",
    "ax.contourf(X,Y,Z,zdir='z',offset=-2)\n",
    "ax.set_zlim(-2,10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the red part in the picture is the area where have the highest probability , and purple part is the area where has the lowest probability.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Final Distribution of Probability\n",
    "Based on the two models we discussed above, flying model and failing model. we get different probability distributions. We want to combine the two patterns in one way . So we will assign different weights to the two models according to the actual situation, to get a final probability distribution.\n",
    "this is the following formula:\n",
    "<br>\n",
    "<center>\n",
    "    $P=w_1p_1+w_2p_2$\n",
    "</center>\n",
    "<br>\n",
    "\n",
    "and $w_1$ and $w_2$ are the appropriate weight, which means:\n",
    "<br>\n",
    "<center>\n",
    "    $0 ≤ w_1, w_2 ≤ 1 and w_1 + w_2 = 1$\n",
    "</center>\n",
    "<br>\n",
    "\n",
    "#### Calculate the Weight\n",
    "we assume that there are two variables, one is H’, the altitude of the aircraft in general, H, the altitude when the aircraft last received the signal.\n",
    "If $H$ is a relatively number close to $0$, then we can assume that the plane has started to crash, then this is a tendency to fall into the model. If H is a value close to the general flight value $H’$, we can assume that the plane is not broken at that time and tends to be the first flight model we discuss. then we have a rate:\n",
    "<br>\n",
    "<center>\n",
    "    $w_1=\\frac{H}{H'}$\n",
    "</center>\n",
    "<br>\n",
    "\n",
    "if $H$ close to $H'$, the rate $w_1 $will close to 1, than means we tend to choose the flying model.\n",
    "if $H $close to 0, the rate $w_1$ will close to 0, than means we not tend to choose the flying model.\n",
    "in this way, we can show the weight in the equation.\n",
    "here we can have the graph of final distribution of probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1141a5a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "fig = plt.figure()\n",
    "\n",
    "# 3d\n",
    "# ax = Axes3D(fig)\n",
    "ax = fig.add_subplot(111, projection='3d') # X, Y value\n",
    "\n",
    "r = np.linspace(0,10)\n",
    "theta = np.linspace(-np.pi, np.pi)\n",
    "w = np.linspace(0,1)\n",
    "X = r*np.cos(theta/2)**2 # the optimistic distribution\n",
    "Y = (10-r)*np.cos(theta/2)**2 # the pessimistic distribution \n",
    "X, Y = np.meshgrid(X, X) # x-y\n",
    "R = w * X + (1 - w) * Y # the final distribution # height value\n",
    "Z=R\n",
    "# rstride: cstride:\n",
    "# rcount:50ccount:\n",
    "#vmaxvmin\n",
    "ax.plot_surface(X, Y, Z, rstride=1, cstride=1,cmap=plt.get_cmap('rainbow')) # zdir : 'z' | 'x' | 'y'\n",
    "# offset : \n",
    "ax.contourf(X,Y,Z,zdir='z',offset=0,cmap=plt.get_cmap('rainbow'))\n",
    "# zxy\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding Model\n",
    "#### Introduction\n",
    "\n",
    "In the two model, we can see that we split the ocean into a square lattice, so the search only needs to search every lattice and starting the search from the maximum probability grid.\n",
    "In our model, the discretization of the search area is carried out under square, and the probability distribution of the location of the downed plane can be ensure with a high probability in an area. In this case, the probability of the downed plane is found in any square is approximately equal.In the $5$ Probability of Containing we consider about where the plane may drop, and in $6$ Finding Model we consider about find. There is a correlation probability of detecting the downed plane for each search container. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Find the ’q’\n",
    "\n",
    "Let $p(z)$ be the probability of finding the downed plane between the search equipment is $z$. Let $K$ be the width of each square:\n",
    "\n",
    "[![444.png](https://i.loli.net/2018/06/23/5b2df6c7c93d0.png)](https://i.loli.net/2018/06/23/5b2df6c7c93d0.png)\n",
    "\n",
    "Let our search go though along a path with the length $L$ divided into $n$ parts and we can get the length of each part is $L/n$.We can make an assumption that the probability of the downed plane follows the uniform distributed. We can fond that the area between the curve p(x) and axis equal to $1$. And the probability of width $K$ is also $1$. For each square with search width $K$, search length $L/n$,($K$ is also the probability that we can find the airplane in the square), the probability of the downed plane can be find in the square is:\n",
    "<br>\n",
    "<center>\n",
    "    $KL/n$\n",
    "</center>\n",
    "<br>\n",
    "\n",
    "For $n$ square, the probability of we can not find the downed plane is:\n",
    "<br>\n",
    "<center>\n",
    "    $(1-KL/n)^n$\n",
    "</center>\n",
    "<br>\n",
    "\n",
    "Therefore, the probability of we can find the downed plane can be find in $n$ squares is $q$:\n",
    "<br>\n",
    "<center>\n",
    "    $q=1-(1-KL/n)^n$\n",
    "</center>\n",
    "<br>"
   ]
  },
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   "source": [
    "### Improving the Model\n",
    "In fact, there are many reasons why it is difficult to find out after the plane is lost its communication. So it turns out that looking for the missing plane is actually associated with a lot of variables. In our model, it’s one of the simplified models that doesn’t take a lot of reality into account. The plane crashed into the sea and for some reason could not be located for long. Perhaps the most fa- mous case was MH370 Malaysia airlines flight and air France flight 447. Although MH370 flights are still missing, flight 447 in the second years after the crash happened founded by a team. the method they used is called: recursive tracking  Recursive Tracking The team is developed and worked on recursive tracking. In short, the method is says: the planes body or its wreckage can be traced on time and this is using a three-dimensional Lagrangian tracking programme.\n",
    "<br>\n",
    "<center>$P_n(\\overline x_{t-\\Delta t},t-\\Delta t) = -\\int^{t-\\Delta t}_t (\\overline v + \\alpha \\overline \\omega)dt + |_n(\\overline x_t,t)$\n",
    "</center>\n",
    "<br>\n",
    "\n",
    "We can use $P_n(\\overline x_{t-\\Delta t}, t-\\Delta t)$ to represent the location of n th object at the time is $t − ∆t$ and $Pn(x_t, t)$ to represent “after ∆t time’s flowing” the position of the nth wreckage. $v$ is representing the veloc- ity vector, $ω$ is the wind velocity vector and α is the wind drag factor. Applying this technology to our model will help to create a more accurate probability representation of the crash site, so as to find the crash site more quickly. This method also allows our model to be used in other situations such as hijacking or deliberate crashes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "We simulate the disappearance of aircraft on radar by dividing the problem into several parts: initial probability model and search model. We found that one of the most important features of this model is to create an accurate initial distribution for the search area. When the initial dis- tribution matches the actual distribution of the crash, the search is summarized faster and more consistently. Because we didn’t get any information after the plane crashed, we had to use the aircraft mechanics knowledge and previous collision accidents to construct the probability distri- bution of the aircraft. With this distribution, we can constantly re-evaluate the probability as we search for different regions. Each of these areas gives us more information to help us create the most effective search areas. We keep updating, because we only start with the smallest amount of information, and even know that it’s useful to combine the possibility of finding the aircraft with the results on the ground. These can have a significant impact on the accuracy of our distribution over time. This feature is also a weakness of the model. If the initial distribution is not close to the actual distribution, it will waste time and other resources searching the non-optimal part of the search area. When we use our previous knowledge effectively to notify our search, be in the best condition of our model using bayesian method is one of the biggest advantages is information is sparse, we can use it effectively. The key to successful search is efficiency. As time went on, it became more difficult to find the wreckage of the plane crash, as the current began to have a significant impact and the search team’s resources dwindled. In general, our model shows that in order to optimize the search result, we should use squares and rectangles to search in parallel, be- cause they cover an area most effectively and can prepare unsearched areas to search in a similar pattern in the coming days."
   ]
  }
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